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. XENON BEHAVIOR IN THE MOLTEN SALT REACTOR EXPERIMENT

 
  
    

   

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This report was prepared as .an account .of work sponsored by the United
States Government.  Neither the ‘United States nor. the United States Atomic
Energy Commission, nor any of their employees, nor any of their contractors,

‘subcontractors, or their employees, makes any warranty, express or imblied, or |

assumes any legal liability or responsibility .for the accuracy, completeness or

usefulness of any information, apparatus, product or process disclosed, or

represents that its use would not infringe. privately owned rights.

 

 

 

 

 
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ORNL-TM-3464

Contract No. W-7405-eng-26

REACTOR DIVISION

J. R. Engel

   

 

= —-———-—-—"" NOTIC E...__..—-—-—————- :
‘| This report-was ‘prepared as  an ‘account of work
‘ sponsored by the United States Government. Neither |.
. | the United States nof the United States Atomic Energy
. | Commission, nor -any-of thei,r.e,mployees, nor any of .| -
‘1 their contractors, subcontractors, or their employees, | -
‘1 makes any warranty, express or implied, or assumes any
- | ‘egal- liability or. responsibility for the .accuracy, com-
| pleteness or usefulness of any information, apparatus,
7 -product or process ‘disclosed, or represents that its use
1 ‘would not infringe privately owned rights. ’ v

XENON BEHAVIOR IN THE MOLTEN SALT REACTOR EXPERIMENT

R. C. Steffy

 

 

L el

OCTOBER 1571

OAK RIDGE NATIONAL LABORATORY

- 0ak Ridge, Tennessee
~ operated by
UNION CARBIDE CORPORATION
- FOR THE

* U,S. ATOMIC ENERGY COMMISSION -

7

 GISTRIBUTION OF THIS DOUMENT 15 URL

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TABLE OF CONTENTS

ABSTRAC';. - e s e . * Q.‘. . . * .I '- L » * . * - . * “ e - . .
INTRODUCT ION * - » * * . * -, .' . - * * - » * - * * * e . - [ -

 

 

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PREDICTIONS BEFORE MSRE OPERATION - . « . . . . .
OBSERVATIONS DURING MSRE OPERATION . . . . . . .

1

2

PROCESSES AFFECTING 1®*XE IN MOLTEN-SALT REACTORS . . . . . . 3
| 6

7

DEVELOPMENT OF MATHEMATICAL MODELS OF MSRE 3*°XE

- DISTRIBUTION

COVER-GAS BEHAVIOR . . v ¢ ¢ o o o o o + o 30
ANALYSIS OF MSRE COVER GAS AND '*°XE BEHAVIOR . 51
 DISCUSSION OF RESULTS . & « & o o s « o o o + 91
CONCLUSIONS v & o v o o o o oo o o v o o s o 95
ACKNOWLEDGMENT . &+ v oo o o oo o o o o o o « 97
REFERENCES « o+ « o o o o s s o o o o o o 0 s 0. 98
APPENDIX « « o o o e o v o o o m o oo o e u 101
 

 

 

 

 

 
 

 

 

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XENON BEHAVIOR IN THE MOLTEN SALT REACTOR EXPERIMENT.

*
J. R. Engel. R. C. Steffy

 ABSTRACT

Since molten salt reactors are based on a circulating fluid fuel, the
possibility exists for continuous removal of ***Xe (by gas-liquid con-
tacting) as a means of impréving their breeding performance. A reasonably
detailed understanding of the xenon behavior in such reactors is essential
for accurate prediction of the removal capability. The xenon poisoning
in the Molten Salt Reactor Experiment (MSRE) was ‘extensively studied in
an effort to develop an understanding of the behavior mechanisms. .

Xenon poisoning calculations made prior to ‘the operation of the MSRE
were based on a mathematical model that neglected any effects of cover-gas
solubility in the salt. These calculations reproduced reasonably well the
observed steady-state poisoning as a function of circulating void fraction
when an insoluble cover gas, argon, was used but they did not adequately
describe the transient behavior. In addition they did not predict the very
low xenon poisoning that was observed at low void fractions with a more

'_ soluble cover gas, helium.

A more'detailed'mathematiCal model which allowed inclusion of cover-
gas solubility effects was developed in an effort to better describe the
observed results. This model successfully described the different poison-
ing effects with helium and argon at low void fractions but it required
the use of mass transport and xenon stripping parameters that differed sig-

‘nificantly from the predicted values. These calculations also failed to
~describe adequately the transient observations. S

A comparison of calculated and observed effects suggests that 1)

- - circulating bubbles may strongly influence the transport of xenon from the
~ fluid to graphite, and 2) both the gas transport and stripping processes

may be affected by operation at power, As a consequence, additional in-

"'vestigations would be desirable to further elucidate the behavior of noble

gases in molten-salt reactor systems.

 

*Curtentlyrassociatediwith Tennessee Valley Authority,,Chattanooga,
Tennessee. |

 
 

INTRODUCTION

The Molten Salt Reactor Experiment (MSRE) was in nuclear operation
from June 1, 1965 to December 12, 1969. During that time the reactor
generated 13,172 equivalent fullpower hours of energy at power levels up
to 7.4 Mw. The reactor system and the overall operéting experience have
been extensively described in the open literature. (Refs. 1 - 4). This
report deals with a specific aspect of that experience, the behavior of
xenon-135. 7 ,.~., - o

Because the fuel is é circulating fluid, the mobility of all the fuel
constituents, including the fiésion products, is an important cpnsideratidn
in the.overall performancé of molten-salt systems. This mobility is
espécially important for the noble-gas fission products because they,:‘
typically, have very low solubilities in molten salts and because some,
~ notably '*°Xe, are significant neutron absorbers. Thus, the potential for
continuous and rapid removal of the gaseous fission products offers the
possibility of reducing both the circulating fission-product inventory and
the neutron losses to ?”Xe.* Although neither of these considerations was
of major significance in the MSRE,. the behavior of '*°Xe was studied ex-
tensively in an effort to develop an understanding of the mechanisms in-
volved. Such an understanding is essential to the reliable prediction of
xenon behavior in other MSR designs. | -

The purpose of this report is to provide a basis for discussion and
then to describe the xenon behavior observed in the MSRE. Since.signifi-
cant differences were found when different cover gases (helium or argon)
were used for the salt, this aspect of the behavior will receive consider-
able attention, We then develop a mathematical model and discuss the re~
sulté of parametric studies whose.objective waé a consistentrdeséription
of all the observed phenomena. Finally some conclusions are drawn about
the apparent xenon behavior and suggestions are offered for experimental

investigations that may further elucidate this behavior.

 

% : ’ '
Calculations for large molten salt reactors indicate that a '*°Xe
poison fraction around 0.5% is desirable for good breeding performance.

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PROCESSES AFFECTING '®°Xe IN MOLTEN-SALT REACTORS

Although many of the xenon behavior processes are the same in a molten
salt reactor as in any other reéctor, the'fact that the fuel is not con-
fined within discrete, impervious elements in the core introduces some
significant differences. The basic procesées for production and removal
of '®*°Xe are outlined in Fig. 1.

The majority of the !23Xe that is produced results from the decay of
the 6.7-hr half-1ife precursor '*?I, At least some of this iodine is pro-
duced by the decay of '®*°Te whose behavior in molten-salt systems is not
completely defined.5 Howe#er, because of its short (29 sec) half-life, Te
has very little effedt/on'th57135’chain. Thus, since iodine has essentialiy
no tendency to leave the salf;s the '®°Xe that is pfoduced directly from
'3%1 is formed in the circulating salt, at a uniform rate around the entire
fuel loop. As indicated on Fig. 1, only about 70% of the '®°I decays lead
directly to '°°Xe and the remainder produce the metastable form, *°>"Xe.
Although the occurrenceiof”this'isomer is unimportant in reactors where all
the fission products are confined within fuel elements, it has potential
significance in fluid fuel systems, particularly if there are other xenon
behavior mechanisms with time constants that are short relative to the
16-min. half-life of the isomer. (Fig. 1 indicatéS—one'such.mechanismé
transfer from the fuel salt into the offgas system.  Not shown, but also
possible, is tfansport into the graphite poresQ) The significance of the
16-minute isomerhis.also_SOmQWhat dependent on its neutron absorption
cross section. Although there are no data available on ;he Cross seétion

of '°°™Xe (Ref. 7), it is,preéfimed'tb'befinegligible-in comparison to that

of 1-MXF.!-.

‘The '3%Xe that is fibt produced by the iodine decay scheme is produced
directly from fission; Literature reports of the fractibn_of'theftotal
13%Xe yield that is produced_directly'in 233y fission range from 3.8%

(Ref. 8) to 18% (Ref. 9). This fraction would be expected to have alfiost
~ no effect on steady-state xenon poisoning but it could significantly\af-

fect the transient behavior following major changes in power level.
 

 

 

 

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Fig. 1. Processes Affecting Xenon Poisoning in a Molten-Salt Reac-

 

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FUEL
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Once the Xe has been formed, it is subject to the same decay and

neutron absorption processes as in any other reactor. Some difference is

‘introduced by the fact thattxendn in the circulating fluid is exposed to a

differentraverage neutren,flux than the xenon in the graphite. However, a

- more important complication is the additional path for xenon removal by

stripping into the offgas ayStem. The reduction in xenon poisoning that
can be achieved depends upoa the extent to which stripping can be made to
compete_fiith the other 1oas&tetms, _In principle, xenon can either be
stripped directly from the citculating_salt into the offgas or it can
transfer to‘circu;ating,bubbles and be removed by a bubble exchange pro-
cess. Thus, the detaills of these two precesses, as well as the rate of

xenon mass transfer between bubbles and liquid are important in describing

.the overall xenon behaVior;t,In addition, any xenon that is transported to

the unclad graphite must be dealt with separately because the xenon inven-
tory in the graphite is.notlavailable for stripping. This process depends
upon the mass transfer from the fluid to the graphite surface and on the

porosity (storage volume) and permeability (accessibility of that volume)

. of the graphite itself.

Another mechanism of potential significance is an abnormal out-of-

- core holdup of xenon, either in_gas-pockets or.on solid surfaces. Opera-

tion of the MSRE showed that there were no significant gas pockets in the
loop except at the reactor access nozzle and the gas exchange with that
region appeared to be too slow to exert much influence on xenon. Holdup

in corrosion-product scales was shown to be significant in an aqueous sys-

~ tem!® because of iodine'adéetption on the scale. ,However, there was no

 corrosion?product scalefih_thefiMSREfand no tendency for iodine to leave

the salt. Xenon sorption on surface active particles that are held out

t'of circulatiqn (possibly in foam in the pump bowl) may also be possible

but will not be considered in this analysis.
 

 

PREDICTIONS BEFORE MSRE OPERATION

Aécurate description of the xenon behavior in the MSRE was an éarly
objective of the project so a considerable part of the reactor development
effort was directed toward this goal The fuel circulating pfimp was ex-
tensively tested in both water'® and molten-salt?? loops to evaluate its
hydraulic characteristics, gas stripping and cover-gas entrainment,
Additional gas stripping tests were performed on a mockup.?® A full scale
water mockup of the reactdr vessel was used to study coté'flbw'pattérns,’“
partly as an aid to evaluating mass transfer processes in the loop. The
MSRE graphite was subjected to a variety of tests'®s® some of which pro-
~ vided data on porosity and permeability which were directly applicable to
the xenon problem. To support these separate studies, an experiment was
performed with the MSRE, prior to nuclear operation, in which krypton was
“injected into'the system and then purged out.!’ The objective of all this
‘work was to provide sufficient data on tfie various mechanisms so that rea-

' sonable predictions could be made of the xenon poisoning.

A mathematical model was constructed to use the available 1nformation
to predict steady-state *>*Xe poisoning in the 'MSRE.!” Since ‘the development
" tests had indicated that there would be a significant fraction of undis-
solved cover gas (1 to 2 vol. %) circulating with the salt, this model in-
cluded the mass transfer of xenon between salt and bubbles and the effects
of bubble stripping. However, early operation of the MSRE with molten
salt indicated that there would be essentially no circulating bubbles

18  Consequently, xenon poisoning cal-

under normal operating conditionms.
culations were made for a variety of circulating void fractions, including
zero. ' r

| In addition to the treatment of circulating voids, several other
apptoximations and assumptions made for this model are ifiportant.' The
solubility of the reactor cover gas (helium) in molten salt was neglected.
With this assumption it was then quite reasonable to treat the entire fuel
loop as a singie well-stirred tank. The production of ®°Xe was assumed
to be uniform around the loop and was confined to the salt phase. That is,

formation by decay of **°UXe was neglected and the direct fission yield

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was combined with the iodine decay term. Since only steady-state condi-
tions were considered, this simplification had almost no effect on the
results. Xenon distribution-in the graphite and the resultant poisoning
were treated in a detailed'(72 region) nuclear model of the core that also
included the radial xenon distribution within individual graphite bars.
However, mass transfer of xenon to the graphite was assumed to occur only
from the salt; direct transfer from bubbles to graphite was not allowed.

The parameter values used and the results obtained from calculations

'with this model are described in detail in Ref. 17. Figure 2 shows one

set of results in which the circulating void fraction was treated as an

independent variable. This figurerillustrates the monotonic decrease in

poisoning with increasing uoid fraction that wasbtypical'of the results

obtained. (Note that in Figure 2 the xenon poisoning is in terms of

233y, Subse-

poison fraction, neutron absorptions in lssXe/absorption in
quent results will use the Xenon reactivity effect, % Sk/k, since this

can be compared more readily with measured values. For the MSRE, the re-

‘activity effect of.a poison‘was approximately 0.8 times the poison

fraction.)

OBSERVATIONS DURING MSRE OPERATION

The behavior of xenon in the MSRE was observed throughout the opera-

tion of the reactor. The primary tool for these observations was the sys-—

19,20

tem reactivity balance’ which was calculated every 5 min by an on-line

computer while the reactor was in operation. This. computation was devel-

oped to provide a real-time monitor of the reactor system for unexpected

'changes in nuclear reactivity. It included calculations of all the known

reactivity changes from'a.reference state as functions of time, temperature,

| power, and fuel loading. All'the'calculated effects, along with the ob-

'served control-rod poisoning were summed and any deviation from zero could

be regarded either as an anomaly or an error in one or more of the calcu-

lated terms. Initially, the only large term in the reactiv1ty balance

with a-significant-uncertainty was the xenon poisoning. _Subsequently, the

accuracy of the other terms was shown by results at zero power with no
 

 

ORNL-DWG 67-1973
BUBBLE STRIPPING EFFICIENCY (%)
0o

138%e POISONING (%)

 

o 0.25 0.50 075 1.00 1.25
MEAN BUBBLE CIRCULATING VOID (%)

Fig. 2. Predicted !3%Xe Poison Fraction in the MSRE with Circulating
Bubbles at 7.5 MW(t).

(w
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2° This information, along with other evidence that no

xXenon present.
anomalous effects were present, allowed us to evaluate the actual xenon
poisoning not only at steady state‘but also during transients produced by
changes in the reactor-power'level and other operating parameters. During
those parts of the operation when there were no (or almost'no) circulating
voids, reactivity'balances'at power were sufficient to define the xenon

poisoning. However, when the circulating void fraction was significant,

' additional data were required'at zero power with no xenon present to permit

separation of the direct reactivity effect of the bubbles.

Although most of'thelkenon'poisoning data were extracted from

reactivity-balance results some supplementary data were obtained from

h samples of the reactor offgas. Since both *3%Xe and *®®Xe are stable

fission products with insignificant neutron absorption cross sections, a

‘comparison of the fission-yield ratio for these isotopes with the actual

isotopic'ratio in the offgas provides a measure of the neutron absorptions

in '®°%e. Such comparisons were made for several samples isolated under

steady-state conditions but the results were too scattered to contribute

significantly to the detailed analysis of xenon behavior. The results did,

however, confirm that the conclusions drawn from the reactivity balances

‘were mnot grossly in error.

Another technique_thatywasattempted'was‘direct measurement of the
‘S’XeVCOncentration:in the reactor offgas at'the fuel-pump outlet using
remote gamma—ray spectrometry. ) When the reactor was operated at high
power the radiation level from the offgas line was so high that consider-

able shielding had to be inserted between the source and detector to ob-

tain manageable pulse conntinéirateSL The effect of this Shielding on
*
the efficiency of the detector system at the energy of the principal '®°Xe

"gamma ray (249. 65 kev) introduced sufficient uncertainty to completely ob-
‘scure the results. At lower power 1evels, residual xenon ‘from previous |

ihigh—power operation had a similar effect., While this technique appears

to offer some promise for studying xenon behavior, additional development

would be required beyond that which was available on the MSRE

 

The introduction of shielding makes this efficiency very strongly
energy dependent below about 300 kev.

 
 

 

10
Circulating Voids. | \usj

Although this report is cdncerned primarily with'the behavior of

- Xenon, that behavior is so strongly affected by circulating voids that a
summary of the experience with voids is presented to prpvide a basis for
”further discussion. A detailed description of the void behavior may be

found in Ref. 21. | .

During the early operation of the MSRE, both in prenuclear tests and
the zero-power experiments, there was no evidence of circulating gas bub-
bles under normal conditions. However, voids were observed when the sys-—
tem temperature and fuel-pump level were reduced to abnormally low values.
Evidence for the presence of circulating voids began to appear after a few
 months of operation at power. A series of prgssure—release tests on the
fuel loop in July_1966.confirméd that some voids were then present even at
normal system cofiditions. Various interpretations of the eariy data indi-

18’22

cated void fractions as high as 2 to 3 vol. Z%. However, as more data

1]

were obtained and evaluated we concluded that the normal void fraction in
the reactor core was quite low — in the range of 0.02 to 0.04 vol. Z.%%2°

Once it became established; the circulating void fraction remained rela- : v
tively constant throughout the ?°U operation of the reactor. Signifi-

cant variationé could, however, be induced by changes i# system tempera-

ture, overpressure, and fuel-pump level. The changes were identified.by

their reactivity effects®*® and by changes in the neutron-flux noise spec-

¢ The results of one series of void-fraction measurements based on

trum,?
reactivity effects are summarized in Table 1.. Because of uncertainties

in the absolute magnitude of the void fraction, the values shown are changes
from the minimum void fraction that was attained. In general, the void
fractions increased with decreasing temperature and increasing préssurea
Although these measfirements did not show any dependence on fuel—pump level,
the associated noise measurements indicated higher void fractions at lower

levels.

 

%

The entire reactor operation with®®°U fuel was carried out with -
helium cover gas and with the fuel circulating pump operating at normal, ( 7
full speed (1189 rpm). ' . \=99
 

 

 

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11

Table 1

Effect of Operating Conditions on Core Void Fraction
- In MSRE with *°°U Fuel?

 

Fuel Pump 'ReaCtdf Ofitlet

Changé from Min.

 

Fuei'Pump
Overpressure . = Temperature Level Range Core Void Fraction

(psig) - (in.) (Vol %)
5 1225 5.6 — 6.2 0
5 1210 5.3 ~-6.1" 10.03
5 1180 5.3 — 5.7 ' 0.11
9. 1225 5.6 — 6.2 0

9 1210 . 5.3—6.0 0.04
9 1195 . 5.3-5.9. - 0.10

9 1180 . 5.3 —5.6 ~0.18
3 1225 5.6 — 6.2 0

3 1180 5.3 —5.8 0.10

“Helium covér gas; 1189 rpm fuel-pump speed.

Based on reactivity effec

t at zero power.
 

12

After recovery of the ***U mixture from the fuel salt and the ad-
dition of 2°°U, the system behavior with regard to circulating voids
changed markedly: the nominal core void fraction went to 0.5 to 0.7 vol. %.
This change, along with other observations prompted a more detailed study
of the void behavior. Some early experiments indicated that, of the para-
meters available for change in:the MSRE, the circulating void fraction was
most sensitive to changes in fuel-pump speed. Consequently this approach
was used to vary the void‘fraction. Figure 3 shows the éffect of pump
speed on the void‘fractiofi for both flush and 2°*U-fuel salts with helium
and argon as the system cover gas. 'Although'we never observed circulating
voids in the flush salt (with helium cover gas) during,the-gssUrfihase of
the operatibn, this salt did develop voids with only a small increase in
fuel pump speed (to 1240 rpm). The different void fractions obtained with
helium and argon apparently reflect thé lower solubility of argon in molten
.salt. That is, for a givén rate of gas.ingestion,at the fuel pump, a
larger fraction of the argon would bé expected to remain undissolved.i The
core void fraction remained relatifiely stable aroufid‘O.S‘éoliz for most of
the 2°°U operation. However, small variations apparently did occur which
had measurable effects on the xenon poisbning; The inability to precisely
define the system void fraction under all operating conditions added con-
siderable uncertainty to the measurement of xenon poisoning as a function
of void fraction. - .

One other aspect of the behavior of.circulating'voids in the MSRE
that will be referred to later is the rate at which the circulating void
fraction could be changed, particularly in the direction of a lower value.
On several occasions, excess circulating voids were introduced by pressure-
release tests or by other system perturbations and, in every case, these
voids subsequently disappéared at a rate which indicated a bubble strip-
ping efficiency of 50 to 100% on the streams passing through the pump bowl.

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ORNL-DWG 69~ 10544

 

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SALT ~ COVER GAS

 

0.7— o FLUSH He

 

0.6

7
® FLUSH. Ar I
& FUEL He
A FUEL Ar :

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LOOP VOID FRACTION (%)
o o
(8] b

 

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0.1 - — 7 ;' I
| .Aiéfxf/{

. 700 800 900 1000 1100
' FUEL PUMP SPEED (rpm)

Fig. 3. _Effecf of Fliel-Pmnp Speed on Void Fraction in Fuel Loop.

1300
 

14

Xenon Poisoning with ?°°U. Fuel -

Since the early operations at the MSRE had indicated that thére were
no circulating voids, the xenon poisoning was predicted on that basis.
Calculations using the model described above showed that, at full power |
(7.4 Mw), the poisoning would amount to about 1.08% 8k/k. When the re-
actor was first operated at power, the reactivity-balance results indicated
that the actual xenon poisohing would be much less than had been antici-
pated. At that time, attempts to use the reactivity balance as an anomaly
detector were deferred (at least during xenon transient conditions) and
the results were used to evaluate the xenon effect. Although this use of
the reactivity balance required the assumption that no anomalous effects
occurred along with the xenon changes, the experience during conditions |

of steady xenon poisoning supported its validity.
Steady-State Values

The first measurements of steady-state xenon poisoning at power levels -

of'S Mw or greater were obtained in April and May 1966. These values and

their associated power levels are listed in Table 2. On the surface, the | .
early values appear to be inconsistent because the highest power is associ-

ated with the lowest xenon value. Little significance was attached to

these differences because of the very large difference between the expected

and observed values and because we had not yet established full confidence

in the reactivity balance. The results were valid, however, and the dif-

ferences are at least.qualizatively explainable. We have already shown

that small differences in system temperature and pressure cause signifi-

cant variations in the circulating helium void fraction and will show sub-

sequeptly that, with helium cover gas, a higher core void fraction leads

to higher xenon poisoning. Both of the first two values were obtained
under conditions that tended to increase the void fraction (i.e. lower

temperaturé at 5 Mw and higher overpressure at 6.7 Mw) so it appears

likely that the different values are attributable to void-fraction vari- -
ations. This explanation is contingent upon the existence of circulating

voids which was not demonstrated until July, 1966. However, there appears ST

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15

Table 2

Early Measurements of Steady State '®*Xe Poisoning
~In MSRE with 22°U Fuel

 

 

_ . Power Level - Xenon Poisoning
Date ;:.rg ~(Mw) - , (% 8k/k)

- 4/28/66 5 O 0.32
5/15/66 . 67 . 0.35

5/25/66 | 7.2 T 0.30

 

to be little doubt that some voids werehpresentat the time these xenon
data were obtained | B |

‘ After routine power operation of the reactor had been established
the full-power steady-state xenon poisoning was between 0.26 and. 0 287
Gk/k for most of the 2y operation. A significant deviation from this
condition occurred during the last major period of that operation, Run 14,
Although much of this run was spent in studying the xenon poisoning under

"different reactor conditions measurements at standard conditions consist-

" ently showed values of 0. 34 to 0,35% 8k/k. Another difference in the sys-—

tem- behavior accompanied this change° the rate of salt transfer from the

 pump bowl to the overflow tank dropped from ~ 1 1b/hr, a value that had
ipersisted for several months, to only 1/2 1b/hr. We suspect that both

changes are related to a change in the behavior of voids 4in the system

but there was no direct evidence for such a change.

 

% T e L _ o -
Unless otherwise noted, the values apply at the "standard" reactor
operation condition: 1210°F core outlet temperature, 5-psig overpressure,
and normal salt level in the fuel-pump tank.
 

 

16

Correlations

Although the reactivity balance was used to obtain data on xenon
poisoning, the primary function of this calculation was to provide a real-
time monitor of the reactor operation for possible anomalous reactivity
effects. Therefore, it was necessary to incorporate an accurate calcula-
tion of the actual xenon behavior, both steady-state and transient, in the
balance. Since the model used for the initial predictions was felt to be
basically sound, we used this modelrto correlate the expefimental data.
The results of these correlations were then adapted to‘the on-line com-
puter. Some simplification of the nuciear representation of the core.was
required to fit the calculation into the on-line system but this did not.
affect the principal characteristics.of the model. |

Earlier development work had established probable values for many of
the parameters in the model and these values were adopted. fiowever, there
were two parameters, circulating void fraction and bubhlewstripping ef-
ficiency, which were not well established for the MSRE'so the effects of
these tworquantities were studied in some detail.* We found fhat the
steady—Statenxenonrpoisoning, as well as many aspects of the'frensient7 |
behafiior‘could be described by adjusting only these two perameters, Fuf-
fhernore, the steady-state poisoning could be described'about4equally well
by-a high circulating void fraction (0’5 to 1.0 vol %) with low bubble-
stripping efficiency (10 to 15%) or a low void fraction (0 1 to 0 15 vol %)
~with a high stripping efficiency (50 to 100%). However, these two sets of
values led to different overall distributions of the xenon. When the void
.fraction wae high, a major patt of the poisoning was &ue to xenon in the
bubbles but, at low void fractions, the xenon in the gfaphife wes the major |
contributor. This difference led'to significantndifferences in the calcu-
- lated nenonAtransienf behavior, parficularly for the xenon removal transi-
ents following a power reduction. With most of the poisoning dne torxenon

in the graphite, the continued-production_from iodine decay in the salt and

 

* o R
These studies were performed off-line using an IBM-7090 computer to

permit greater flexibility in the calculations.
 

)

)

(.,

 

17

transfer to the graphite after the reduction in power (and burnout in the
core) tended to produce a peak in the xenon transient. Then, after the
xenon in the fluid had been depleted by stripping, xenon diffused out of
the graphite and was stripped so that rate of change in poisoning was more
rapid than it would have been if only radiocactive decay were operative.

As the poisoning shifted toward the circulating fluid, with increasing void
fractibn; the xenon peak tended to disappearffrom the decay transient. In
addition, the low'stripping'efficiency'required_to match the steady-state
poisoning slowed the rate of decrease in xenon poisoning.

When the observed transients were compared to the calculations, we
found goad agreement with the IOvaoid—ftaction, high-efficiency curves.
Figure 4'shows one example of the quality of fit that was obtained.
Furthermore, the void fraction appeared to be consistent with other, inde-

pendent observations. ConseQuently, this model, using a 0.15 vol % void

 fraction and a 50% bubble stripping efficiency was used for the on-line

Xenon calculations. These calculations produced good results through

Run 12 of the 235U operation (August, 1967). It will be recalled however,
that this model did not treat cover—gas solubility effects, nor did it
provide for variations in the circulating void fraction with reactor oper-
ating conditions. Thus the empirical fit to the xenon poisoning was ap-
plicable only to the specific reactor conditions under which it was es-
tablished. Although this limitation was clearly recognized when the
calculation was developed, the sensitivity of the reactor xenon poisoning
to . system conditions was unknown until actual measurements were made in

Run 14 with 232U fuel and still later with 23°U fuel.

‘Effects of Operating Parameters

 

A subject that was investigated extensively in the MSRE was the corre-
lation between the core void fractionrand the neutron-flux noise spectrum.?*®
One objective of that work Was to develop neutron noise analysis as a diag-
nostic tool for measuring'the;VOid fraction. A series of special tests was

performed in teactof_Run_léito'futther this effort. The tests involved

- operation of the system at various temperatures, overpressures, and fuel-

pump levels, first at near-zero power (no xenon) so that the reactivity
 

18

ORNL-DWG 67-1087

 

 

 

a6 — @ EXPERIMENTAL DATA ,OBTAINED ——]

- \ ' DURING MSRE RUN NO. 10

 

 

0.4 / T,

 

 

 

\\
\ N,BUB‘BLE STRIPPING
. -

 

 

 

REACTIVITY MAGNITUDE (% S 4/4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

03 \ EFFICIENCY (%)
-8

L™ 1T Y I 10 |

\ "“0 W\
' 1 | \%F‘o\ 50 | T~

Xy

as e L
100 @ —g _._.;_;.
0 1
0 4 8 12 16 20 24 28 32 36 40

TIME AFTER DECREASE IN REACTOR POWER LEVEL thr)

Flg i, Effect of Bubble Stripping Efficiency on Transient Decay
of !'35Xe Reactivity. Step decrease in power level from 7.4 MW to 03 vol %
circulating bubbles, 0.15. ' -

 
 

 

 

")

19

balance could be used to measure the void fraction, and then at 5 Mw to
measure the noise spectrum. The effects of the operating parameters on
void fraction have already been discussed. However, when the reactor was
at power, additional reactivity differences were observed which, because
of their reversibility and time constants, could only be attributed to
changes in xenon'poisoning.'

Figure 5 shows the effect of tne nominal core void fraction on xenon
poisoning at 5 Mw, withoutgregard for the changes in operating parameters
that were made to vary the void-fraction.' Although there is considerable
scatter in the data, the trend toward greater xenon poisoning at higher
void fractions is clearly evident. There—are several possible reasons for
the scatter but these have not been evaluated quantitatively. First, the
measurements-of nominal void.fraction and xenon poisoning were separated in
time and we have no direct assurance that a given set of operating condi-
tions always produced precisely the same core void fraction. Second, the
void-fraction measurement is subject to considerable uncertainty in this
range because of the small reactivity differences involved (0.02% 8k/k for
a void-fraction change of 0.1 vol %). And, finally, we have ignored the
fact that different'ccmbinationsiof parameter values wery used to obtain
the void fractions (cf. Table i)‘so the direct effects of these parameters
on the xenon behavior are included in the data scatter. Thus, while Fig. 4
illustrates an important aspect of the xenon behavior in MSRE, it does not

provide an adequate basis fcr_modification of the xenon model.

 

Xenon Poisoning with 2°°U Fuel

Possibly the most significant difference in the MSRE operation with

_233U fuel, as regards the xenon behavior, was the drastically different

~ volume fraction of circulating voids under standard conditions. As indi-

cated_earlier,.the void fraction changed from 0.05 vol % or less, with ?°°U

fuel, to about O;S_VDI'ZQ"The;precise reason for'thisgshift has not been

established but it may have;been'caused by different physicai_properties

(density and, possibly, surface tension and viscosity) of the two salt mix-

tures. It has also been suggested®’ that an accumulation of insoluble
 

20

ORNL-DWG T1-8032

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4
g
. _
¢
°
03 2
»,
¢ e
e
:; $
o0
® ¢
& o0
; ®
z °
z -
Q0.2 :
o
a ¢
= ®
o
=
W
>
04
0
0 , 0.1 0.2

coae VOID FRACTION (%)

Fig. 5. Effect of Core Void Fractlon on MSRE Steady-State Xenon
Poisoning at 5 MW with 235U Fuel.
 

)

al

c

21

metallic particles —-fissiofi and corrosion products — into a "scum" on the
surface of the salt pool in the pump bowl could have contributed to the
change in void behavior. In any event, this change ultimately led to a
complete reinvestigation of the xenon problem.

The first step in this investigation was to establish the behavior of
the voids as such. This was greatly facilitated by the installation of a
variable-frequency generator to supply power to run the fuel pump at dif-
ferent speeds* and prelimifiary measurements were made of the effect of
fuel-pump speed on the core void fraction with helium cover gas. We then
attempted to measure the steady-state xenon poisoning at various void frac-
tions. The void fraction was adjusted by regulating the pump speed and the
reactor power was held to 7'er This allowed us to make all the measure-
ments at one reactor outlet temperature (1210°F) without reaching undesira-
ble temperatures in other parts of the system. In addition, the system
overpressure and fuel-pump level were restricted to narrow ranges. The
results of these xenon poisoning measurements are shown in Figure 6. Con-
siderable uncertainty must be assigned to the void fractions between 0.1
and 0.3 vol Z. These pointeiwere obtained with the variable-frequency
driverrunning near, but not'et,.ite;maximum speed capability and difficulty
was enceuntered in controlling'the speed precisely. The extteme sensi-
tivity of the void fraction:to'pump speed in this region (cf Fig. 3) prob-
ably caused the void fraction to wander during the tests.

The early data on void fraction and xenon poisoning were obtained in
March 1969,.during Run 17, the_first'period of high-power operation with
??°0 fuel. These data were used to adjust parametervalues in the existing,
on-line xenon calculation.to provide better steady-state xenon.values, Two

sets of parametetslwere'developed for use'with.high and very low void

- fractions. As reactor operation continued, it became apparent that this

approach did not adequately describe the xenon behavior. Then, a scheduled

reactor shutdown in.June,f1969 added another dimension to the xenon problem.

 

“The generator was installed to permit an investigation into the ef-
fects of fuel—pump speed and void fraction on the occurrence of small power
disturbances.?
 

22

ORNL-DWG 69- 12619

 

 

 

 

 

 

 

 

 

 

 

 

.08 - t :
¢ POWER : 7 Mw
COVER GAS:HELIUM
g s
< 06
§ ®
g o
& o
E 0
9

§ - v
& 02

0

° o2 04 06

AVERAGE CORE VOID FRACTION (%)

Fig. 6. Effect of Core Void Fraction on Steady-State Xenon Poisoning
(Measured in March 1969). | | .
 

al

)

23

One of the operations planhed for the shutdown was a replacement of

corrosion and surveillance specimens in the reactor core. Since this

- operation required opening of the reactor primary loop, the normal pro-

cedure called for filling the loop with argon to help prevent intrusion
of air and moisture during the replacement. On this particular occasion
the introduction of argon was started ~2 hr before the reactor power was
reduced. For several days prior to the shutdown, the reactor had been

operating at reduced fuel-pump speed (and slightly reduced power — 7 Mw)

to minimize the circulating void fraction. (The off-design operation was

~adopted to prevent aggravation of a restriction in the reactor offgas sys-

tem which was also scheduled for correction during the shutdown.)_ As argon
replaced the normal helium cover gas, there was.a substantial decrease in

the nuclear reactivity of the system. This decrease was later shown to be

associated with a marked difference in xenon poisoning, at low void frac-

tions, with the two cover gases.
When reactor operation was resumed, in August 1969, an extensive series

of experiments Was'performed to_elu¢idate the circulating void behavior at

 Various fuel-pump_speéds with both helium and argon cover gases and to
_evaluate the Xenon poisoning with both gases. By that time, also, the

-speed-control problems with the variable-frequency power supply had been

largely corrected so that the'data,at intermediate void fractions were more
reliable. These data provided the principal basis for the reevaluation of

the xenon behavior in the MSRE. However, the data collection continued

- into September and the reactorjdperation was terminated on December 12, 1969.
HConsequently; the revised analyéié'described in this report was not used

~during the reactor operation..

The effects of fuel-pump speed and cover gas on the circulating void

fraction have already been discussed ‘(see Fig. 3). The measured effect of

*
- the core void fraction on xenon poisoning with ?°°U fuel at 5 Mw is shown

 

‘in the reactor power level as determined by system heat balances
-uranium isotopic changes in the fuel salt,>°® It now appears that the iso-

* | - o S SR ' e
This power has also been reported as 5.5 Mw because of a difference
le *% and by

topic-change evaluation is probably more nearly correct, so the proper level
for these xenon measurements is 5 Mw.
 

 

 

24

~in Fig. 7. The results with helium cover gas show essentially the same
behavior as those obtained earlier with this combination. In addition,
the results are at least qualitatively similar to those obtained with 2°5U
fuel at low void fractions. In contrast, the results with argon cover gas
show a significantly different behavior at the lower void fractions. These
data appear to demonstrate the monotonic decrease in poisoning with in-
creasing void fraction that was predicted by the model which neglected
cover-gas solubility. However, it should be noted that there is a sighi-
ficant gap between the pbint shown at zero void fraction and the next data
: point. In addition there is some uncertainty about the void fraction at
which the first point should be plotted. | |
During the collection of the xenon data, as in all reactor operations;
there was some variation in the fuel-pump level because of salt transfer to
the overflow tank. And, while the level effect was small, if there was any
tendency for voids to be present in the core, that tefidency was enhanced at
the lower salt levels. Figure 8 shows the progress of a xenon build-in
transient as a function of time after a power increase from 10 kw to 5 Mw.
This test was performed with argon cover gas while the'fuelépufip speed was
800 rpm. The reactor outlet temperature and system overpresSfire were at
their normal values, 1210°F and 5 psig respectively. At normal pump-bowl
salt levels, these conditions corresponded to zero void fraction in the.
core. Also shown in this figure is the indicated salt level in the fuel
pump bowl. It may be noted that, as the salt level decreases toward 6 in.
(relative to an arbitrary zero reference), there is a change in the shape
of the xenon curve. At about this same time, 25-30 hours into the transient,
the neutron noise, as indicated by an analog instrument that recorded the |
average (RMS) level between 0.6 and 1.4 Hz (Ref. 31) began to increase.
By3the time some of the salt was returned to the pump bowl (at 44 hf), the
noise level had increased by a factor of_2, suggesting a small but steady
increase in the core void fraction. The noise decreased somewhat, but_not
to its original level, when the salt level in the fiump bowl was raised and
then increased again with decreasihg salt level. The appareht variation
in void fraction with salt level indicated by the neutron noise was quali-

tatifiely consistent with previous experience at other pump speeds and salt
R

 

ekt

25

ORNL-DWG 69-10545R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

" CORE VOID FRACTION (%)

Fig. 7. Effect of Core Voi.d Fraction on Steady-State Xenon Poisoning
(Measured in August—September 1969).

C

1.0 -
55 Mw
-~ o HELIUM
= e ARGON
o8
«@©
3
Z 08 2
.z .
8 8
O O
S 04 1°
=
Qo o
- & 02?
x e
- 0 -
- - 0 - Of 02 ©03 04 05 06 07
 

 

 

26

ORNL-DOWG 71-8033

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70

% -

5 *ea, ® e g
E.J‘G.O il LLYIN 2ea,] * .."‘o.--
d g ® ohe ®
oY % SALT RETURNED TO FUEL PUMP

50 FROM OVERFLOW TANK |

— OE.

3

~ .

5 -0.2 > 'S

- &

9

L %

& -04 -.%

“ *

> 08 “e

= =006 o,

g =

]

o ®

g -os :

™ Sgta,
e T
-10
0 10 20 30 40 50 60 70
‘TIME (hr)

Fig. 8. Xenon Buildup Transient with Argon Cover Gas and Low Cir-
culating Void Fraction.
 

 

*»

&

27

levels. Figure 7 shows clearly a decrease in the magnitude of the xenon

reactivity effect that followed the increase in salt level and a subsequent

increase in poisoning as the salt level dropped. A somewhat similar oc-

currence had been observed about a week earlier with the fuel pump oper-
ating at 900 rpm. However, in the earlier case the salt-level effect on
the xenon was partly obscured by a change that was made in the gas purge
rate through the pump bowl. |

Although the events just'described are not readily subject to quanti-
tative evaluation, they strongly suggest that the xenon behavior with de-
creasing void fraction'was similar for both helium and argon cover gases.
The major difference'apfiears to have been in the value of the decreasing
void fraction at which the xenon poisoning curve began to turn down and
in the extent of the decreasé'in-poisoning{' Figure 9 shows what now ap-
pears to be a better representation of the effect of core void fraction on
Xenon poisoning in the MSRE with»argoh cover gas. The shaded area at low
void fractions is infended’tb show only the region in which the xenon poi-
soning apparently varied, rather than to indicate the precise nature of
the variatibn. | | - |

Agide from the speciai'experiments performed”to evaluate xenon poi-
soning, routine observations weie made of the xenon effect throughout the

2350 operation, variations were

223U operation. As was the case in the
observed in the steady-state xenon poisoning that could not be assigned to
known changes in the operating_¢onditions. Table 3 shows some of the values

that were observed at full power and otherwise nominally standard condi-

tions. Minor deviations from the Standard 5-psig overpressuré did occur

but these do not appear to account for the xenon changes. It seems more

- 1likely that minor changes-in-théifuel-Salt'properties allowed the void

fraction to wandér enbugh-to vary the xenon poisoning. The nature and
magnitude of the changes required to produce the observed variations is

unknown.
 

28

ORNL-DWS 71— 8034

 

10

 

o
o«
\§
N
N

 

o
o

 

o
s

 

XENON POISONING (% 34/k)

o
N

 

 

 

 

 

 

 

 

 

0 0.4 0.2 0.3 0.4 05 06 0.7
CORE VOID FRACTION (%)

Fig. 9. Adjusted Variation of Steady-State Xenon Poisoning with Argo
Void Fraction. 7 | .

 

 
Iy

 

 

29

Table 3

Full-Power Xenon Poisoning

During **°U Operation

 

 

Xenon

Date Poisoning

| (% Sk/k)
2/21/69 0.36
2/25/69 0.36
4/15/69 0.32
4/18/69 0.40
10/6/69 0.51

10/20/69 0.39
11/29/69 0.44
12/11/69 0.45

 
 

 

30

DEVELOPMENT OF MATHEMATICAL MODELS OF MSRE
133XE AND COVER-GAS 'BEHAVIOR

The approximations and assumptions made in earlier mathematical models
to describe xemon behavior in the MSRE were discussed earlier. Since the
net effect on the overall results was not obvious, we included a large
number of individual mechanisms in the model to be déscribed in an effort
to see if particular aspects of the observed xenon behavior could be
related to specific mechénisms.

Although we wére céncérfiédrpri;arily-fiith the faté_of xenon, it was
a basic premise of thié‘approach.that the xenofi behévior was dependent
on the_behavior.of.the cover gas. Thus, it washhecessary to include in
the xenon model a description of the cover-gas conaitions around the loop.
This description cou1d be computed within the ienon model for the cases
where an insoluble cover gas was assumed. However, when significant
cover-gas solubility was allowed, the non-linear cerr-gasbehavior was
computed separately and the results used aé input for the xenon calcu-
lations. In this section we describe first the kenon model and then the

model used to compute the cover-gas conditions.
Xenon Model

As a first step toward increasing the fléxibility of the xenon model,
the fuel loop which previously had been treated as a single, well—stirréd
tank was divided into several regions. This made it possible to consider
the approximate* effects of short term dynamic mechanisms such as the
compression and expansion of circulating gas bubbles.as well as gas
dissolution in and evolution from the liquid. In addition, the core
region was subdivided into 4 radial regions to allow for different rates
of mass transfer due to the radial profile of fuel salt velocity through

the core. This subdivision also permitted a radial breakdown of the xenon

 

*

A lumped-parameter model such as this is still only an approximation
to the real case but it is much more manageable than a more accurate
distributed-parameter model would be.
 

31

burnout and poisoning effects. There was no subdivision in the axial di-
rection but axial‘effects were accounted for by using average neutron
fluxes and nuclear importances for each radial region.

Figure 10 shows sehematieally'the subdivision of the reactor loop
that was used for the mathematiCal_description and the material flow-paths
that were considered. :The subscripted variables within each block refer
to the concentrations of *®3I, !®%Xe, and ®°MXe that are applicable to
each_region. In general, a'time-dependent material-balance equation of

the form

dXi ."

3 jZ.IAij g0 171, .. 24
was written for each dependent variable in each region of the model. The
resultant set of 24 linear, first-order differential equations could then
be solved for either the steady-state solution vector or the timeidependent

behavior, as required. In the sections to follow, we discuss the mechanisms

‘and terms that were includedlin these equations. However, the final equa-
“tions with all their repetitive terms are relegated to the appendix. They

~are printed on fold-out sheets so that the interested reader may have them

beside the text for ease in following their development. The form in which
the equations are presented was selected in an effort to make the various
mechanisms more readily apparent. It should be recognized that this is
neither the most compact form attainable nor the one required for their

solution by a computer.

_PumpiBowl, .

As indicated by Fig.lo"three"regions were used to describe the

xenon behavior in the pump bowl' ’the'gas space above the liquid the

liquid phase, and a separate ‘gas phase to represent bubbles that enter

from the main loop and return to- that loop without losing their identity

(1. e.‘are ‘not stripped)

- The major xenon inputs to the pump-bowl gas space are the bubbles

stripped from the salt flow through the bowl and direct mass transfer from
 

 

32

ORNL-DWG 71-8029

PURGE : OFF

 

 
 
  
 

 

 

 
 

 

 
 
 
 
  

 

 
   
 
  
 

 
     
  
  
 

 

GAS = GAS :
PUMP BOWL SUBSCRIPTS
135_1 135x€ ISSmXe'
GAS
X,  SPACE 13 2 |
4 3
6 5
e 7
OLD 10 9
Xy Xi2 BUBBLES 12 T
19 | 15
16 19
LIQUID 6 2
‘ 18 23
22
24

 

 

 

 

  
  
 
  
      

 

  
   

   
   
   
  
 

GAS
BUBBLES

X7

GAS
BUBBLES

Xarl

LIQUID
X9

       
    

     

| PIPING AND |
PIPING HEAT EXCHANGER

    

  
 
  

  
  
  

Xz X20 X8

     

X3

 
 
   
  

REACTOR CORE

    

X0

   

X3 LIQUID

  
 
   
 

GRAPHITE

      

X15

   

Xig | X17] %16} Xia

     

Xoz Xoq

 

GAS BUBBLES

  

Fig. 10. Lumped-Parameter Model for Xenon Calculations.
33

the liquid pool. An additional source term for '®°Xe is provided by the
decay of *°°MXe already in the gas space. Since iodine is presumed to
remain entirely in. the salt phase, it does not contribute to the xenon
sources for this region. The salt flow through the pump bowl is composed
of the actual stripper flow plus the leakage or "fountain" flow around the
pump shaft. These flows are treated separately in the model and separate
bubble-stripping efficiencies are assignable to each. The actual xenon
inputs are thus defined by the gas inventory in the preceding region, the
flow rates, and the stripping efficiencies.

Direct transfer of xenon from the 1iquid pool to the gas space is

described as a mass-transfer process in this model. That is, for '3°Txe
, o | %*
.Sl' = thC (Xs - HRTX1) s

and the comparable term for *3°Xe is obtained by replacing Xs and X, by
X, and X2, respectively. Since this mass transfer process is not well
defined, we arbitrarily assigned it the same coefficient that was used for
'“gas-liquid_trafisferS'in'the remainder of the system. The effect on the
xenon balance of veriations.in'the'fate of mass transfer was examined by
verying the effective transfer area, Ac. This area was probably quite
large (tens of square feet) because of the agitation and cover-gas carry-
under produced by the spray ring. However, the extent to which the gas
that is carried under (but not ingested into the circulating loop) mixes
with the gas above the salt probably depends strongly .on the amount and
stability of the foam in the. pump bowl. ' The presence or absence of a
scum of non-wetted, noble—metal fission products on top of;the liquid®?

~ could also be expected'to'havetSOme effect. Another factbrtthat very
‘likely influences xXenon stripping is the evolution of cover—gas ‘from the
salt. - If a significant amount of cover gas can dissolve in the salt in

- the loop, there will be tendency for that gas to escape from solution

f__while the salt is in the pump bowl which, in turn, may affect tfle Xenon

 

 

 

rescape rate. All ‘of these effects are lumped together in the choice of

 

% |
Symbols are defined in the appendix.
 

 

34

‘a value for Ac. Thus this approach fails to distinguish between several
factors that are capable of influencing the liquid stripping but it does
retain the dependence of the overall process on the xenon concentration
in the gas space. The net efficiency of,the-liQuid stripping process is
easily extracted from the results by comparing the xenon concentrations
in the salt streams entering‘andlleavifig the pump bowl with that in the
gas phase. - '

The xenon sinks for the pump-bowl gas space are radioactive decay,
the cover-gas purge.to the offgas systém, and covér gas ingestion into
the fuel loop. The first two mechanisms are cofipletely defined by the
region concentrations, the decay constants and the net cover-gas purge
rate. However, the amount of cover gas that is drawn from the gas spacé
into the fuel loop must be extracted from a cover-gas material balance. |
For a soluble cover gas, the total gas phase flow may be determined by a
~ separate calculation that includes consideration of the gas in solution
in the‘salt.* Of this total gas phase flow, part is unstripped gas that
simply passes through the pump bowl without mingling with that in the
gas space. (The xenon in these "old bubbles" is tféated'separately below.)
The volumetric flow rate of old bubbles into the loop is defined by the
- flow rate from the loop and the bubble stripping efficiency, along with
. consideration .of the bubble size and the manner in which that size is
attained. _ ; ,

In general, as bubbles approach the pump, they have been reduced
from their original size by compression and cover-gas dissolutiqn in the
salt. Some of this size reduction (all of it for an insoluble cover gas)

is recovered by expansion as the bubbles return to the lower pressure in

the pump bowl. In this treatment we have assumed that all the bubbles
have been restored to their original diameter by the time they are re-

‘turned to the loop. For a soluble cover gas, there are two mechanisms

 

. Throughout this analysis we have neglected the contribution of xenon
to the volumetric and mass flow rates in the gas phase. Mole fractions of
xenon in the cover gas are 10~ or less in all regions.
 

....,‘__,.*.._........_..‘.M......

35
/ | | | ,
that could contribute to this size restoration: agglomeration with other
old bubbles and growth by entry of cover gas from the fuel salt. These
two mechanisms represent extremes of the range of possible effects on the
xenon behavior so, both are examined (Merger of the bubbles with gas
from the pump-bowl gas space to increase their size has an effect between
these two extremes.) If the size restoration of the old bubbles is allowed
to occur only by agglomeration with other old bubbles, the flow rate of
this_stream‘to the ioop is thesame as the unstripped part of the flow rate
from the loop. Then the flom rate from the pump bowl gas space into the
loop 1s | | |

F o= YR 4P -V, B2 R -e) +F -ep]-F,

where the first term on-the right represents the total gas phase flow

into the loop and the second term is the contribution to that flow from

. the old bubbles. If the old bubbles return to their original size by

collecting cover gas from the salt, the old bubbles contribute more to

_the total flow and

Yoyt Fp) = ¥s [F (L= ) + (= e - F,,

fn

or

F Tg(Fe +F )--F.'

It may be noted that if the cover gas 1is insoluble

oy, B2 ooy

Ps 3

" and the two expressions are eqoimalent. In each of.the'above'equations
_'for F the final term allows for the direct ingestion of clean purge gas
~ before it has an opportunity to mix with any of the other gas in the pump
~bowl, It has been suggested that at high void fractions (high rates of

gas ingestion) the gas flow from the bubbler level elements ‘may be drawn

directly into the loop.

The principal difference between the two approximations to the be-
havior of old bubbles is in the effect on the xenon concentration in those

bubbles, which is discussed below. The effect on the flow of pump-bowl
 

36

cover gas into the loop is small except at high bubble sttipping effici- -
encies with a soluble cover gas. Eveh at these conditions, the effect on
F can be approximated with the first expression by increasing the size of -
the term Fe. Consequently we used the first expresSion to describe the
"gas flow into the loop from the pump-bowl gas space.
‘Equations 1 and 2, Appendix A, are the final rate'eQuationé for the
concentrations of °*PXe and *>°Xe, respectively, in the pump bowl gas
"space. In these efiuations, as in all'equéfiions in the set, the region
volume is included in the terms on the right-hand side to convert the
absolute rates discussed above to rates of concentration change.
The treatment of the liquid region in the pump bowlris largely typical
of the treatment of all the liquid regions. That is, there are xenon
source terms from liquid flow in, from decay of '®%I and, in the case of
135%e, from decay of *®°™Xe. The sink terms include liquid £low out,
xenon decay and mass transfer to the gas phase. Since the gas in the pump
bowl is treated as two separate regions, cover gas and old bubbles, two | .
separate expressions are required to describe the mass t;ansfer. The twb _
expressions use the same value for the mass transfer coeffiéient'but they
are otherwise independent. That is, the direction of xenon transport (to
or from the liquid) is defined within each expression by the magnitude of
the relevant concentrations. The rate equations for *?°®Xe and '*°Xe in
the pump-bowl liquid are Eqs. 3 and 4, ’
The treatment of the old gas bubbles in the pump bowl has largely
been established by the preceding discussion of the cover-gas space. The
primary xenon source for this region is the inflow of unstripped bubbles*
which is defined, as before, by the inventory in the last upstream region,
the flow rates and the assignéd stripping efficiencies. The flow rate of
~ xenon into this region-due to the flow of unstripped bubbles is:

 

* ' |
For '®%Xe, the source from the decay of '*°®Xe must also be
included. - '
 

37

w,,[Fg(i - e) +F (- el

However, this is an absolute rate so it is necessary to consider the

volume of the bubble region in order to establish the effect of the xenon

input on the region concentration. This volume depends upon the choice

of the mechanism for restoration of the bubble size. If only agglomeration
with other old bubbles is allowed, the volume is readily obtained from the
entering bubble concentration and the liquid volume'in'the pump bowl.

That is ' - |

F'(i-e)'+Ff(1-e'

 

| )
: - P ' o ; £
Via .-"'-. Yie | 1;: S_ B ;S T Ff Vs_-

If the unstripped bubbles maintsin their individual identities and grow

by absorbing cover .gas, the region volume follows from the number concen-

tration of the bubbles and their ultimate size. (In this lumped-parameter

approximation, the bubbles are assumed to reach their final size immedi-

~ ately upon entering the pump. bowl ) Since bubbles are assumed to maintain

their identities in the loop, the number concentration in the salt stream
entering the pump bowl is defined by the total rate of gas ingestion into
the loop and the referencebubble.diameter. The.total number of.unstripped
bubbles that remain in the salt in the pump bpwl is then ginen by

o, [F (1L-E )-kF‘(l-E )
Nia =,1/6 d"'l- _ FS.+F

 

Vs.
£

The total volume occupied by these bubbles (which now also,hafie the ref-

~erence diameter) is

.Fs(lf“ ES) + Ff(l "Ef)
©wF_ +F
8

 

. ' . ,
: V1.1- = : ?_3 - VS! )
f :

The entire term for xenon'flow'into'this region is then either
 

38

F +F
[_V: 1 21(22)

or

| -- -EI.D ‘
‘?1_,91 . Ps (FS + Ff)

 

.; wsvs : xzx(zz)'

depefiding on the mode of bubble behavior that is aseumed.

The xenon sink terms for the unstripped bubbles in the pump bowl are
the gas flow out to the loop and radioactive decay, As we indicated
earlier, the absolute magnitude of the gas flow rate of old bubbles back
to the fuel loop depends on the mechanisms that are allowed for the bub-
bles. This absolute rate was required to obtain the net cover-gas flow
rate in Eqs. 1 and 2, However, the time constant for gas flow out of this
region, or the freetional;rate of throughput, is of interest here and this
is ptesumed to be defined by the 1iquid flow rate and the volume of the
liquid pool in the pump bowl, Hence, the term that describes the effect
of the exit gas flow on the xenon concentration in the old bubbles is in-

dependent of the assumed bubble behavior.
| The concentration of xenon in the old bubbles depends on the mass
transfer between them and the pump bowl liquid. . Thus, if these bubbles
grow by agglomeration, the surface area for mass transfer tends to decrease
but the xenon concentration (driving force for mass transfer) tends to
remain high. Conversely if the bubbles grow by absorbing cover gas, their
number remains constant and the surface area increases while the xenon
concentration decreases. The areas for mass transfer under these two
alternatives are readily obtained from the region volumes and the reference
bubble diameter. However, it should be noted that the quantity of interest
is the time rate of change of xenon concentration within this region. Thus,
the absolute mass transfer term, which is a function of bubble area, is
divided by the volume of the same bubbles. Consequently, with either al-
ternative, the mass transfer term is reduced to a product of the bubble

mass transfer coefficient and the surface-to-volume ratio of the bubbles.
 

 

 

[} '
‘. o

39

Since spherical bubbles are assumed the latter factor is simply the
constant, 6/d o '

, Equations 11 and 12 describe the overall xenon behavior in this
region of the pump bowl for the assumption that agglomeration of the un-
stripped bubbles occurs. Since the changes required fOr'the alternative
assumption about bubble behavior have been described the second form of

these equations is omitted

Piping == Pump to Reactor'Core

The entire section from the fuel pump to the reactor core, including
the primary heat exchanger was treated as a single unit in this analysis.
This region also includes the salt downcomer in the reactor vessel and
part of the lower head. Two pairs of equations were required one pair for
the liquid phase and one for the gas phase. Since the heat exchanger was
not treated separately, the effects of changing temperatures around the
100p on factors such as gas density, gas solubility, and mass transfer
coefficient are neglected in this model . Most of the xenon data were
accumulated with the reactor‘at 5 MW where the temperature spread in the
'primary loop was only 25 F so the neglect of such effects probably has |
little effect on the comparison of calculated and observed xenon behavior.
| The xenonybehavior in the liquid phase of this region is described
by Eqs. 5 and 6. The general treatment for‘a liquid phase'has already been

 discussed and this same treatment was applied to the region in question.

The only distinctive feature 1n thls particular region is that the incoming
_salt originates in two regions, ‘the main loop and the pump bowl with

different xenon concentrations.. ‘Thus two terms are required to ‘define the

" xenon source associated with salt flow in.

The treatment of the gas phase (Eqs. 7 and 8) is somewhat simpler than
“in the pump bowl in that there are no gas exchange processes to be con-
sidered. Although gas_enters ‘the region at three xenon concentrations from

three sources, this is readily°aCCounted for in the three source terms.

- Xenon exchange with the salt phase by mass transfer is represented by a

' single term in each’ equation. o

 

The numbers of the equations became scrambled in the original develop-
ment but, since the solutions are independent of the order of presentation,
the numbering system used in the computer program is retained here.
 

 

40

Reactor Core

Several equations 'are required to describe the phenomena in the re-
actor core. This is due partly to the introduction of neutron-flux de-
pendent effects but prlmarily to the presence of the graphite subregions.

The liquld phase (Eqs. 9 and 10) is again treated as a single region
but with an additional source term to account for direct lssXe production
from fission and a sink term for the burnup of '®3Xe. It is assumed in
this that all of the direct production is **®Xe (no '*°UXe) and that the
neutron absorption cross section for '°°™e is negligible. In the case
of 135Mye, the mass transfer between the salt and graphite is described
by a single term on the assumption that the effect of this isomer is small
enough that small errors in describing it will have little influence on
the overall result. The mass transfer coefficient used is that normally
assigned to the bulk (98%) of the graphite. The use of 4 regions to

'®°Xe in the graphite dictated the use of

describe the concentration of
4 terms to represent the mass transfer of this isotope into the graphite.
This breakdown also permitted the applieation of a different mass transfer
coefficient to the central graphite region where the fluid-flow velocity
is higher. 7 '

Equation 13 describes the behavior of *°I in the entire reactor loop.
It is included here because the entire iodine source is treated‘as direct
production from fission in the core. Since the half life of iodine (6.7 h)
is very long compared to the transit time for salt in the fuel loop (26 sec),
only a single iodine concentration is computed for use in all regions of
the model} The volume in which the iodine is dispersed is the entire salt
volume in the loop. | |

Five equations (14 through 18) are used to describe the Xenon concen-
tration in the graphite. As indicated earlier, only a 51ng1e concentration
1s used for '?°™Xe while four regionel concentrations are computed for
1%°%e. Equation 15 deals with 135W%e while Eqs. 14, 16, 17, and 18 treat
the '?°Xe in the 4 graphite fegions. Both isotopes are presumed to enter
the graphite by direct flow of cover gas into the graphite as well as by
mass transfer from the salt. The salt mass transfer terms have already

been discussed in connection with the core liquid phase. The entry of
 

 

 

« T

41

cover gas into the graphite is treated as an exchange process in which
circulating gas bubbles that enter the graphite are replaced by an equal
number of bubbles at the xenon concentration near the graphite surface.
The gas flow into the graphite is apportioned in the same way as the fluid
flow through the core. The only sink term for '®°®Xe in the graphite is
its radioactive decay while both decay and burnout are included for *°®%Xe.
In principle, the sink terms within the graphite lead to a.radial
concentration profile in each stringer that has a minimum at the center.
If the stringers are regardéd as cylinders the radia1 profile at steady
state is described by |
. I _(Br)
C(r) = ¢ T§T§§T s

where:

~ C, = xenon concentration at the graphite surface,

R = -equivalentiradius of the stringer,

Ié = zero-order modified Bessel function of the first kind, and
-
B = o (¢0 + X).
. G

The average radial concentration, still at steady state, is'given by

= _ 2 LR
© 7 R TR R

Thus, for the steady-state'coh&itiofi, it does-not'add-significantly.to

the complexity of the problem to describe the xenon exchange mechanisms

5with\the'f1uid in terms ofithefSurface-concentration-and-the internal
. mechanisms (burnout, decay, poisoning) in terms of the average concen-
. tration. The factors required to include this effect are not shown in

~ the equations but they were added to the computer program for the steady-

state calculatiohs. Earlier studies had indicated that, for the materials
 

42

and conditions in the MSRE, the xenon profilé in the graphite stringers
had a negiigible effect on the overall results. The same conclusion was
reached in this study. | :

‘Some allowance was made in the model for radial diffusion of !33Xe
- between the major graphite regions. Since this process was expected to
have only a minor effect on the overall results, it wés given a relatively
superficial treatment. A diffusion-type expression was used with the
effective graphite area between adjoining regions and th¢ center-to-center
distance between them. - | ' '

The xenon concentrations in gas bubbles in theléore are described by
Egqs. 23 and 24. The mechanisms associated with the varibus'terms have all
been discuSsed previously and these discussions willrnOt:be‘repeafied here.
It should be noted, however, that the possibility of complete dissolution
of the cover-gas bubbles was allowed for the core regioh'ih this model.
(Non-zero void fractions were required in all the other regions.) VWhen
this condition was attained, these equations were eliminatéd and the re—
maining 22 equatibns,'whiéh then hompletely defined the system,fwere

*
solved.

Piping -- Reactor Core to Pump

The usual conditions assumed for the xenon calculations included
cover-gas bubbles in the core region. In these cases, the treatment of
the piping from the core back to the fuel pump was essentiélly the éame
as in the other piping'region discussed'previously; the only differénce
is that here only one term was required to describe the gas flow into the
region. The equations that define the xenon Behaviorfin this section are
Eqs. 19 and 20 for the liquid and Eqs. 21 and 22 for the gas. However,
when complete bubble dissolution was allowed in the core; a different
source term was required for flow into the gas region. In such cases it

was postulated that the specified void fraction developed spontaneously

 

* : - .
It should be noted that, under these circumstances, an additional
source term was required in the core liquid equations to account for
xenon entering the liquid from the bubbles in the preceding region.
 

 

 

 

.

43

in the piping section and that an arbitrary fraction of the xenon inven-
tory in the salt appeared with the bubbles. A further requirement was
that the new bubbles appear at'the same number concentration that existed
in the remainder of the system. The xenon flows into the liquid region
were then reduced by the amount of the flow into the gas region. Although
this process is not very realistic from a physical standpoint, it provides
a reasonable approximation when used in a lumped-parameter model. The
modified equations to deal with this special situation are shown as Egs.
19a through 22a. |

Nuclear Considerations

Although the primary purpose of this report is to examine the effects

of a variety of non—nuclear parameters on the xenon behavior, nuclear

burnup of **®*Xe is a significant_mechanism in this overall behavior. In
addition, the principal'compariSOn between calculated and observed behavior
is made on the basis of the reactivity effect of the xenon. Therefore, it

is necessary to use at least an internally consistent treatment of the

nuclear effects in the model., The absolute accuracy of this treatment is

of relatively minor importance because any errors simply produce changes

in scale that are only slightly affected by the choice of other parameters.

As we will show later, the pattern of xenon behavior is defined largely by
the non-nuclear parameters so‘comparisons of these patterns'do not depend

heavily on the nuclear model

Xenon Burnup —-Burnup is assumed to depend only on the average concen-
tration and effective neutron absorption cross section of the xenon and the

average neutron flux in any particular core region. That is, local vari-

‘ations in flux due to the presence of the xenon are neglected Published

values®® of the effective cross section and average flux in the MSRE with

233y fuel were used in this model, - Since the fluid phases (liquid and gas)

'were each treated as single regions in the core, the core averaged neutron
‘fluxes were used directly.: However, regionally averaged fluxes were re-
"quired for- the various graphite regions. These values were obtained from

the radial distribution of the thermal flux at the core midplane and the

region radii defined for the xenon model with normalization to the overall

average flux,
44

Reactivity Effect — The reactivity effect of xenon is defined by the
following equation: : :

R = nY Xe.
(Gk/k)Xe aX o s

= the reactivity coefficient for a neutron absorber

a
X = the overall, importance-averaged concentration of '®°Xe, and

cze = .the effective xenon absorption cross section.

{ , i
The value of @ for the **°U fuel loading was taken as -174 for thie
study.® For the MSRE core, in which the graphite volume fraction is 0.775,

the average concentration is given by

0.775
G

 

X = 0.225 [(1 - ¥s5) Xio + ¥5 Xa24] + [I:4 Xaa + Ii6Xae +

I,7X37 + I1eX16]

where

TG = the graphite void fréction and

I = the relative nuclear importances of the graphite regions.
Because of the similarity of the neutron flux shapes with the ?°°U and **°vy
fuels, relative importances that had previously been evaluated for the 23°U

loading®® and the same geometry were used.

Bubble Models

..Throughout the foregoing discuésion of xenoh behfivior, the volume of
undissolfied cover gaé in each 1iqtid region of the model was treated as a
kndwn quantity. For the case 6f a totally insoluble gas, the void frac-
tions and the bubble surface areas are completely specified by selecting
a core void fraction and a reference bubble diameter. Variations in the

void fraction around the loop are produced only by differences in the total
 

 

 

 

45

pressure in the wvarious regions and these are known. Thus, for an insol-
uble cover gas, the factors describing the void fraction were incorporated
in the xenon calculations:themselves. 'Howéver, when mass transfer of
cover gas between the gas and liquid phases occurs, the void fraction in

a given region depends on a number of variables: gas solubility, residence
time, mass transfer coefficient, bubble_érea, and concentrations. Since
the equations required to treat the cover-gas conditions are nonlinear, it
was expedient to calculate separately'thé void conditions and then use
those results in the_xenon calculations. Furthermore, we were concerned
primarily with the xenon behévior ét established void-fractions so only
the steady-state void éonditions were calculated.

The lumped parameter fiodeli Fig. 11,;used to describe the cover-gas
conditions used essentially the same loop regions that wére used in the
xenon model. However, the existence of fewer behavior mechanisms for the
cover gas, along with the need to deal with only one gas, considerably
simplified the mathematical treatment. In the pump bpwl‘we assumed that
all bubbles drawn. into théi¢1#¢ulatifig loop Were of the same reference
size. (The same assumption was uséd in the xenon mddel;) Since the cover
gas.cohéentration, or partial pressure, in these bubbleé wés-defined by the
system overpressure, bubbles of unstripped cover gas from the loop were
identical with new bubbles from the gas space and directly ingested purge
gas. Therefore, only_onefregion was_required to describe the gas in the
pump. In the liquid fegion;it was apparent that the dominant term for
stripping dissolved gas was the contacting with the coverégas region so
only one mass—transferftérm'wastused,__The assumption in the core that any
cover-gas transport (by @aésnyfqpsfer ot direct flow) into the graphite was
balanced-by an équivalentflow'béék_tothe_fluid in the cbré'completely.

- eliminated the graphite frofijconSideration in the steady—state afialysis of
the cover gas'conditions.-iThé diécussion, below, of thé éQuations used to
calculate the bubble cbnditidhsifollows'the same general course és.that
'fot the xenon equations.' Héfie?er,'the_subscript numbering'éystem was
changed to conform to the smaller number of variableé in this model.

~ Briefly stated, the model is required to compute the void fraction in

each of three regions of the loop from an assumed void fraction, or rate
 

 

46

ORNL-DWG 71-8030

" PUMP BOWL

 

 

 

 

 

 

 

 

 

 

 

VN AR S SR A A A AR B R A A

] A
3 M
f GAS SPACE /
4 Zy :
M : :
A

1
f 4
1 '
: LIQUID [
I Zz. ‘I’z : :
A

 

 

 

 

 

 

 

 

 

 

 

 

-—
=\L/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 N ! e ! ]
f l:As [ g IGAS !
f CLuip | 1 LiQuiD /
| | zg fe—ed 27| [jProine CHEAT f | T3 fa—d 2. |
, v | | EXCHANGER[l | w, [ ] "% | |
A , 9
' : ! :
| 5 4 : f :
’ ) M

 

 

 

 

 

 

REACTOR CORE

gl E T

 

 

 

 

 

 

<

LIQUID
Zs, ¥s

 

 

.

 

 

 

 

GAS BUBBLES
Ze /

 

 

=

 

 

 

 

ToT T T T E T T d oo

 

 

 

 

 

Fig. 11. ' Lumped-Parameter Model for Cover-Gas Calculations.
T e i e i 4 g
‘1

 

 

47

of cover-gas ingestion in the pump bowl. - Since these void fractions depend
on the amount of gas dissolved in the liquid, the gas concentrations in the
four liquid regions are also dependent variables. The gas concentrations
in the bubbles were treated as known quantities. Thus, we have 7 inter-
dependent variables which require 7 material balance equations for a com-
plete description. Equations 25 through 31 were used for this purpose.

In general, each term is written as a combination of constant coefficients
times a function of the dependent variables. The number of terms contain-
ing two dependent variables is an indication of the degree of nonlinearity
of the equations,

Equation 25 describes tfie time rate of change of cover-gas concen-
tration in the liquid in the pump bowl. The first term is the source due
to liquid flow into the region while the second term represents the liquid
flow out. The final term répresents the rate at which cover gas is
stripped from the liquid into the gas space across a surface area, Ac’
defined by the agitation in the pump bowl. Mass transfer'between/the
liquid and old or unstripped_bubbles-wasneglected since the driving force

for such transfer would be the same as for transfer to the gas space and

the available area was much smaller. In this region, as in all liquid

regions, the appropriate volume is the'volume of 1liquid in it. In the
pump bowl, this is defined by the amount of foaming or agitation rather
than by the rate of gas ingestioh into the loop. Hence this volume was
allowed to be independent of the void fraction in the stream returning to
the loop. In the other liqfiidregions, the tdtal volume is fixed by the
region size and an.adjfisffiént:must be made for the void fractions that
exist there. s e | - o o

- Equation 26 deScribéé ;he1conditions-in the first liquid region down-

stream from the pump. de;térmSIare required to differentiate between in-

flow from the main loop'andjinflow from the pump_Bowl;'the:third term
represents flow out. The mass-transfer term depends on the area that is

”available and this afea'1s'éxpté53ed'inAterms of the void fraction as de-

scribed below. o
Throughout this treafmént wé'assume-that'each bubble in the loop main-

tains its individual-identity at all‘times.' Then the number concentration
 

 

 

 

48

of bubbles in the circulating fluid is defined by the rate of gas ingestion

and the reference bubble size:
J

N o s
Yo mgeE

The total bubble area in any region is then

A, = N 1rd3

i i i
or
1 2
. 6 Y, di i
8y T d
' -1
However, at constant N
.
4.4
4 fa

or
L et
dR(‘l’i/‘Yz) .

Then substitution into the expression for Ai leads to

A = 6/dy ‘l’z \r'i'vi
Since the final equations are wribten in terms of concentration, the
region volume cancels out in the final expression.

The next two equations, 27 and 28, treat the remaining two liquid
regions in the same way as those already discussed.

The remaining'equations (29, 30, and 31) describe the void fractions
in the three regions ofithe fuel loop. In each case the_first term (two
 

terms in Eq. 29) represents the flow .of undissolved gas into the region
and the next term represents the flow out. The final term in each equa-
tion describes'the'mass transfer between the gas and liquid phases.

We indicated earlier that the cover gas concentrations or partial
pressures within the bubbles are regarded as known quantities. This im-
plies_that the gas pressure inside a bubble is a function of the liquid
static pressure only. LIn géfiéfai‘ the total pressure inside a bubble is
the liquid static pressure plus a contribution due to the surface tension

of the liquid That is. o

For the MSRE fuél salt, the'surfacefltension effect is ~0.4 psia on a 10-mil
diameter bubble and ~4 psia_on—a 1-mil bubble. Thus, for very small bub-
bles, the driving force for mass transfer out of (or, therresistance to
mass transfer into) the bubble increases sharply with decreasing diameter
and very small bubbles tend to dissolve completely. ' Such dissolution
would tend to supersaturate the liquid and cause other, larger bubbles to
grow in size. This process'may'impose a lower limit on the size of the
bubbles that can circuIate_with'the'salt. However, the effect on the over-
all void behavior is small. For the initial bubble sizes considered in
 this analysis (around lO'miiS),-by'the time the bubbles have been suffici-
ently reduced in size by dissolution‘for'the surface tension effect to be-
come important, so little gas inventory remains in the bubbles that its
transfer to the liquid has a. negligible effect on the 1iquid concentration.
' Therefore, in cases ‘where bubbles_exist in all regions of the model, the
surface tension effect OnVCOuer gas bubbles is neglected. Complete disso-
lution is, however, still allowed in. the xenon model where it must be

treated as a special case anyway.

 

e . N L | :
‘If the liquid itself has a significant vapor pressure, the gas
partial pressure is reduced by that amount.. However, the fuel-salt vapor
pressure was entirely negligible at the conditions encountered in the
MSRE,
 

 

50

Solution of Equations

Computerized orocedures for solving.thefabove systems of equations
were largely availaole. The purpose of this section is simply to indicate
the general methods and_prograns used_to_obtain the_required solutions,

| Steady-state solutions for the non-linear equations used to describe
the behavior of a soluble cover'gas were obtained with a pseudo Gauss-
Seidel technique;* The typical computing time required to obtain a solu-
tion was 1 sec on the IBM 360/75. No transient solutions were obtained
for these equations since each xenon calculation was made for a fixed
void fraction. | ‘ -

- Two types of solutions were obtained for the xenon equations., Steady-
state solutions were adequate for most of the xenon parameter studies,
these were obtained with the aid of an ORNL library subroutine MATQ
which solves the simultaneous, linear algebraic equations that result
from the'assumption of steady state. The-time required_for such solutions
‘was typically 2 sec on ‘the IBM 360/75. Xenon buildup and removal transi-
ents were calculated with MATEXP.%¢ Normally, the transient was calculated
~ for 40 hr in time increments of 0 015 min, These solutions required aboutrr
- 4 min of computer time on the IBM 360/91.__Because of this long computing
time, only a limited number of transients:was calculated. The results of
each xenon calculation, steady-state or transient, were converted to reac-
tivity within the computer programs

One of the more time-consuming tasks associated with the use of the
above computer programs was the calculation of the individual terms in the
coefficient matrix for the xenon equations. A computer subroutine was
written to calculate the coefficients from the various input parameters.
This subroutine also made the necessary conversions from the various

engineering units used with the input parameters to a consistent set of

 

'This approach was suggested by C. W. Nestor and implemented by
T. J. Tyrrell, both of the ORNL Mathematics Division.

o | -
MATQ is an ORNL adaptation of the CO-OP subroutine MATALG which uses
Gaussian elimination with partial pivoting to produce the solution.
 

51

metric units. Thus, the problem ‘could be specified in familiar (but mixed)
units without the need for multiple manual conversions. ‘This routine pro-
duced a coefficient matrix that could be used by either MATQ or MATEXP, as

required.

ANALYSIS OF MSREQQOVER GAS AND **°XE BEHAVIOR

The mathematical models described in the preceding chapter were used
in an extensive calculational study to- see what combinations of the various
mechanisms and parameter values were required to calculate xenon behavior
modes like those observed in the MSRE - Of particular interest in this re-
gard was the -very 1arge difference in the variation of the steady-state
- xXenon poisoning with core void fraction when argon was ‘substituted for
helium as the system cover gas. Consequently, a large part of the study
was aimed at describing this phenomenon. In addition to the steady-state
calculations we performed a number of xenon transient calculations to try
to verify the results of the steady-state correlations.

- In the ensuing sections of this chapter, following a general discus-
~sion of the_parameter-variations that were allowed, we describe first the
calculated variation in the cover-gas void fraction dround the MSRE fuel
loop when solubility effects'are’included. In.addition to supplying needed
input for the xenon calculations, these results provided a basis for re-

~ stricting the ranges of somesparameters. We found, for example, that the
initial bubble diameter (within a reasonable range) and the salt-to-bubble

mass transfer coefficient had 1itt1e effect on the void fractions in the

. rest of the loop for a given core void fraction. Consequently the xenon

 

 

' calculations were all made for void fractions established for 10-mil bub-
bles with a mass transfer coefflcient of 2 ft/hr. _

. With the cover gas behavior~established, we proceed with a discussion
of'the'steadyéstate 135%e calculafions;-rThe first step is to show that,
for similar parameter'valuesfand'angin861ubleicover gas, the model that
‘we, have developed givesessentially the same results as those predicted
by earlier models. ' We then show that simply adding cover-gas solubility

effects to these parameters, even with wide variations in bubble stripping,
 

52

is inadequate to describe the observed steady-state '*°®

Xe poisoning with
helium cover gas. At this point we introduce an additional mechanism for
xenon transport to the graphite and show that this mechanism;~élong with
what appear to be reasonable xenon stripping parameters, produces results
that fit the reactor experience with both helium and argon covef’gas.

The final section of this chapter describes the results of xenon
transient calculations. One purpose1of'fhe‘transients was to see if para-
meter values that appeared to describe the observed steady-state xenon
fioisoning could also describe the dfiserved ttansiefit‘behavior. These cal-
pulatidns were fegarded as further tests of the'adequacy of both the model
and the parameter valueé,. The transient éalculations»also-provided a means
for separfiting the effects df some of the pérameteré; It was fofind that
some parameters which had almost no effect'pn the'steady-stafe reéults

~could significantly affect the transiénts.
'System Parameters

The various physical parameters required to describe the xenon behavior
- have already been discussed, at least implicitly, in the development of the
mathematical equations. However, the model was developed in a way that

would permit its application to systems other than the MSRE. Thereforé,_

- . many of the quantities that are required as input parameters are defined

 

by the physical description of the MSRE and the operating conditioms.
“Additional parameters are fixed by the physical properties of the materials
involved and the mechanisms that are considered. These considerations
still leave a number of parameters that can be allowed to vary over rela-
tively wide ranges in the calculations. .It was clear that purely arbitrary
selection of even these parameter values would be capable of describing

any and all xenon results. Therefore, restrictions were imposed on the
selection of values., For parameters that were allowed to vary with void
fraction, the basic principles involved in the variation were applied
_equally to the calculations with both cover gases. All parameters were
required to vary smoothly with the void fractionm. That.is, discontinuities
or reversals in functional dependencies were avoided, Table 4 lists all the

parameters that were involved in this study. Most of these quantities were
 

 

53

Table 4

Parameters Used to Calculate Xenon Behavior in-MSRE'

Definition Units Value

 

Fixed Parameters o | (Range)

Absolute pressure in model region:

1 | | : psia 19,7
3 . " : 19 .-7
5 ' - ' : " 46,1
9 ' B o . " - 37.9
14 through 18 : ' | " : 37.9
19 _ " . ) 32.7
Fluid volume in model region o |
1 | £t® 1.5
3 " 3.2
5 " 28.8
9 ' ' " 25.0
19 e ; " 13.5
Gas volume in model region:a | '. - S
14 S o ft® R 0.137
- 15 : . " . ' 6.918
16 - " 1,133
- 17 _ ' " 1.916
18 - | " 3,732
Fluid Flow Rates | |
| Total salt flow . o R ~ gpm - 1200
Salt through spray ring e "o 50
Salt fountain flow T oM 15
‘Gas purge of pump bowl ; - &/min -~ .~ 8,08
Fractional salt flow rate through region. R SRR
16 | e | - - - 0.,0198
16__ | e - - . 0.1673
17 3 ' L - 0.277
18 o LT - - " 0.5395
Salt—to-graphite surface area in region: | S
14 R T O f* 3041
15 (total) ' IR T " , 1520
17 _ . o . : " 421.0

18 - o o 820.0

 

%Baged on 10% accessible void volfime in graphite.
 

54

Table &

(continued)

 

 

bAssumes 18% of total '*°Xe yield is direct.

®Yariations in this parameter investigated separately.

Based on a fluid volume fraction of 1.0. -

Definition Units Value
(Range)
Graphite—to—graphite surface area _- -
between regions: |
14 and 16 - f? 4.5
16 and 17 " 10.8
17 and 18 " 15.9
Direct fission yield of *3°Xe bse atoms/Mw-Sec 3.437 x 10**
Direct fission yield of 1351b,0 " 1.567 x 10*°
Fraction of '°°I decays to **Txe° - - 0.3
Fraction of **°I decays to 13538 - 0.7
Decay half-life of:
1331 min 402
13%mye " 15.3
135%e " 552,
Burnup Coefficient for *>°Xe in Region:
9 (salt or voids) (mw sec)~? 4.75 x 10™°
14 (graphite) " 5.76 x 10~°
16 " " 7.29 x 107
17 " " 6.47 x 10™¢
18 " " 3.09 x 10~°
Reactivity Coefficient of **°Xe in Region: |
9 (salt or voids) (6k/k) (atom/cec) =0.517 x 10~*'®
14 (graphite void space)® " -0.791 x 10—*®
16 (graphite void space) " -0.669 x 10-17
17 (graphite void space) " ~-0.699 x 10~'7
18 (graphite void space) " -0.334 x 107
Henry's Law Constant for Xenon moles/cc~atm 3 x 10-°
| Henry's Law Constant for Helium " 1.26 :t:_lO"’7
Loop temperature °F 1200
Graphite diffusion coefficient ft?/hr 10-“ - 10~7
il 4,

 

 

 

 

 

55

Table 4

| :(continued)—

Definition

 

Reactor Power

Mw

Units Value
, o | o (Range)
Effective Radial'Qistance;Between'Regions .
14 and 16 in. 5.95
16 and 17 " 7.4
17 and 18. " 7.95
Variable Paraneters
Mass Transfer Coefficient, salt to gas - ft/hr 1-15
Mass Transfer Coefficient, salt to graphite _ |
- 1in bulk of core ft/hr 0.01 - 0.18
Mass Transfer Coefficient, salt to graphite SR ,
in central core region (14) ft/hr 0.06 - 1,14
Area for Mass Transfer from Salt to Cover |
Gas in Pump Bowl ' \ ft2 -0 -700
Reference Bubble Diameter in, 0.005 - 0.020
Core Void Fraction® | % 0.02 ~ 0.7
Bubble Stripping Efficiency for: '
| Spray Ring Flow | % 0 - 100
'Fountain Flow % 0 - 100
Direct Bubble Flow to Graphite £/min 0 - 2.7
Clean Cover Gas Flow into Loop £/min 0 - 0.6
- 0.01 - 8

 

Void fractions in other regions were calculated to be consistent

that in the core.:

with
 

 

56

used as direct input to the computer programs. However, some of the values
'weré combined to reduce the total amount of input required. The first part
of the table lists those parameters that were fixed, or at least limited to
narrow ranges for most of the calculations. The second part includes those
parameters whose values were manipulated in the course of the calculatiomns.
In both cases the values or ranges of values are listed with the parameters.
Some of the parameter ranges are quite wide and many calculations were made
which failed to produce the desired results. In the following sections we
will describe only those results that best illustrate the conclusions.

Cover Gas Calculations

As we indicated in the development of the equations for the'cover—gas
model, the purpose of these calculations was to define the circulating void
fractions in the various regions of the xenon model. Since these calcu-

. lations are significant only for a soldblé gas, this section deals only
- with the conditions for helium cover gas. (In this study the reactor re-
sults with argon were compared to computations made with an insoluble
cover gas, for which the void ffactions were evaluated Withinrthe Xenon .
_model itself.) | |

The helium void fractions in various regions of the system model are
best described in terms of the ingested void fraction; that is, the void
fraction in the salt returning to the circulating loop from the pump bowl.
This quantity was variéd from 0.05 to 1.5%. Other parameters of interest
were the initial size of the bubbles, the rate of helium stripping from
the liquid in the pump bowl, and the coefficient for mass transfer between
the bubbles and the liqfiid. It may be noted that bubble stripping effici-
encies arevimmaterial because, in a single gas model, all the bubbles have
the same-composition and all are presumed to enter the loop at the same
size. _

Figure 12 shows the calculated void fractions in the three regions of
the circulating loop as a function of the ingested void fraction for three
initial bubble sizes. These curves were calculated for a fixed mass trans-
fer coefficient between bubbles and liquid in the loop.. Since the liquid \
stripping is represented as a mass transfer process with the same gas- k";

liquid mass transfer coefficient that is used for bubbles in the loop,

d
 

 

 

 

 

Al

1.0
7 0.9
0s
0.7
0.6

0.5

LOOP VOID FRACTION (%)

0.3
0.2

04

0.4 F

57

ORNL=-DWG Ti~-8035

 

 

   
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IR
MASS TRANSFER COEFFICIENT ,
BUBBLES TO LIQUID : 4 ft/hr
™™ PUMP BOWL LIQUID STR;PPING
COEFFICIENT : 240 ft%/hr
INITIAL. BUBBLE SIZE : oog?sggén M
— === 5 mils
{0 mils
= 20 mils
CORE
UPSTREAM
OF CORE
o - 05 1.0 1.5

INGESTED VOID FRACTION {%) .

Fig. 12. Calculated Helium Void Fractions in MSRE Loop — Effect of

Ingested Bubble Size.
 

58

the significant parameter in the pump bowl is the product of that coef-
ficient and the effective interfacial area. This product is designated

as the pump bowl liquid stripping'coefficient, a constant for Fig. 12.
This figure illustrates that the circulating void fraction is relatively
insensitive to bubble size, at least for the conditions thafi prevailed in
the MSRE, This is due at least partly to the fact that, as the fluids
travel around the loop, the mass transfer changes from diséolution of gas
in the liquid to evolution of gas from the liquid. Thus, the gas and liq-
uid are never very far from an equilibrium condition. -

The most significant feature of these curves is their displacement to
the right of imaginary straight lines, with similar asymptotic slopes, that
pass through the origin. The lines through the origin would describe the
behavior of an insoluble gas so, the displacement is a measure of the
amount of helium dissolved in the salt. Subh helium dissolution tends to
concentrate any xenon ingested with the bubbles and thus reduces the capa-
city of the bubbles to accept xenon from the salt, This effect tends to
becofiermore important at lofi void fractions where most of the ingested gas
dissolves. |

It may be noted that, although the curves are nearly straight over
most of the range, they all break toward the origin at very low wvoid
fractions. This bending reflects a limitation in the model which allows
bubbles to exist at all diameters. If the effect of liquid surface tension
on the bubbles had been included, the curves would have intersected the
abscissa at the point where complete dissolution occurred. Thus, this
model does not accurately predict the amount of gas that must be ingested
_ to attain very small void fractions. However, for the values considered,
the surface tension effect becomes significant only for very low void
fractions as illustrated by the following example.

The calculation for 10-mil bubbles predicts a void fraction of 0.088%
in the region upstream of the core when the ingested void fraction is 0.5%.
This reduction in void fraction implies a bubble size of 5.6 mils in that
region for which the effect of surface tension on the internal bubble
pressure is 0.71 psi. The-helium concentrations are such that the driving

force for'gas dissolution is 7 psi. Hence, inclusion of the surface-~tension
 

 

59

effect would have changed the driving force by only ~10%. These and other -
similar figures indicate that the calculated helium void fractions are
reasonable for core void fractions down to 0.05 to 0.1%Z. At lower values,
the calculation tends to underestimate the amount of helium that must be
ingested to achieve a given void fraction in the éore.

Figures 13 and 14 show the effects on the circulating void fractions
produced by variations in thé coefficient for mass transfer between the
liquid and bubbles in the loop. The results are shown on separate figures
to avoid some of the line ifitetseétioné near the origin. These results are
for a single initial bubble éize and a fixed stripping coefficient in the
pump bowl, Although there is little dependence on mass transfer coef-
ficient in two of thé'tegipns, the effect is quite pronounced in the region
just upstream of the core;‘_Ihis results not only from the closer approach
to equilibrium with the highér coefficient but also from a shift in the
equilibrium void fraction.. As'would be expected, the higher mass transfer
coefficient allows better hélium stripping from the 1liquid (and the devel-

opment of a highér void fraction) in-the region downstream of the core.

- Some of this liquid is then subjected'to_furthet stripping in the pump bowl.

Then, when the two liquid streams are merged to enter the region upstream

~of the core, the liquid has a greater capacity to accept helium from the

bubbles, which leads to a,lowét_equilibrium void fraction in that region
for a given rate of gas ingestion.

Figures 15 and 16 show the effects of changing the rate of gas strip-
ping in the pump bowl. (Again; two figures are used to present the results

for the three regions only injtfie.interest-of clarity,) These figurés show

that the void fractionsrarerfét more sensitive to changes in stripping than

to either of the other two patémetérs considered. This sensitivity is due

. primarily to the greater'capacity of the liqfiid to accommodate gas after

it has been more thoroughly stripped in the pump bowl._'
The liquid stripping rates used to produce these curves were defined

in,terms of a mass_transfer;coefficient and an effective interfacial area.

However, other_authbrs (Ref;il7)rhave'described this generai process in

terms of a "stripping efficiency." This efficiency is defined as the ratio

of the change in gas concentration experienced by the salt flowing through
 

60

ORNL-DWG T1-8036

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.8 — » T T
INITIAL BUBBLE SIZE: 10 mils
PUMP BOWL LIQUID STRIPPING
0.7 |—  COEFFICIENT : 240 ft3/hr .
MASS TRANSFER COEFFICIENT, /
. BUBBLES TO LIQUID : ., //
0.6 I— - | §1/hr /)
| - — 4 fi/hr - 7/ /7
= ——— 24 ft/hr L/ /
.E _ ) 16 / ’
(z) 0.5 27V
. = . . Y/ N .
- /
2 /
. m . ‘0
& 0.4 ’
a | : /7 ./ .
g : ' .‘/’/
u o3 . vy A
O ,’/
S . ,
7\
0.2 vy -
, .
r’ .
. i / /
0.1 y —4 v
-
0 o ,
0 0.5 1.0 .5

INGESTED VOID FRACTION (%)

Fig. 13. Calculated Helium Void Fractions in MSRE Core — Effect of
Mess Transfer Coefficient.
 

 

61

 

 

 
 
 
 
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ORN
1.0
"INITIAL BUBBLE SIZE: 10 mils
PUMP BOWL LIQUID STRIPPING
L— COEFFICIENT: 240 ft%hr
MASS TRANSFER COEFFICIENT,
BUBBLES TO LIQUID:
0.8 = e § ft/hr
4 ft/hr
— e 24 ft/hr
g .
g 0.6
[y
O
<
(14
'
o
g
Q 0.4
&
a
0.2
o ’
0 - 0.5 1.0 1.5

INGESTED VOID FRACTION (%)

Fig. 14. Calculated Helium Void Fractions
of Mass Transfer Coefficient.

L~-DWG 71-8037

DOWNSTREAM
OF CORE

UPSTREAM
OF CORE

in MSRE Piping — Effect
62

ORNL~-OWG 71-8038

 

1.0 | [ T

INITIAL BUBBLE SIZE: 10 mils
MASS TRANSFER COEFFICIENT,
— BUBBLES TO LIQUID: 4 ft/hr

 

PUMP BOWL LIQUID
| STRIPPING COEFFICIENT:
——— 40 ft¥/hr

- 240 13/hr /
— e 480 t>/hr /

 

0.8

 

 

 

O
N
~N
|
N\
N

 

o
H
\ .
N
N
N\
\\
- N

 

CORE VOID FRACTION (%)
N,

—f—
////‘

"V /

 

 

 

 

 

 

 

 

 

 

 

/
' ¢

0.2 // // //

/|
1/ y. I'
A /17 _
/ A
0 z o ™
0 0.5 1.0 1.5

INGESTED VOID FRACTION (%)

Fig. 15. Calculated Helium Void Fractions in MSRE Core — Effect of
Pump-Bowl Liquid Stripping.
 

 

63

ORNL-DWG T!-8039

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 | R T
INITIAL BUBBLE SIZE: 10 mils /
MASS TRANSFER COEFFICIENT, /
| BUBBLES TO LIQUID: 4 ft/hr 7
PUMP BOWL LIQUID STRIPPING / DOWNSTREAM
COEFFICIENT: /. J[oF core
0.8 |~ === 40 ft3/hr
240 13/hr -/
— - 480 f1¥hr //
) /
— / ,’
g / / /
g os / £
= /777
g UPSTREAM
c / /L7 o core
o 7 /
g A / .// //
2 04 / L
L / A 7
1/ /'/ /r
/ A /I . .
/ A/
/ /¥
O 2 / . Fi 2
. / ‘7 '/
- / /? ’/
/ /1 A ! ,/ -
2 ,flf
v\ L
0 Y 1.0 1.5

INGESTED VOID FRACTION (%)

Fig. 16. Calculated Helium Void Fract
Pump-Bowl Liquid Stripping. -

ions in MSRE Piping — Effect of
 

 

64

the pump bowl to the change that would occur if equilibrium were estab-

" lished between the gas and liquid phases., Since the calculations of the
“.void fractions also produced liquid concentrations for each of the regions,
such stripping effiéiencies are readily extracted from the results. The
correlation between the stripping coefficients employed in these calcula-
tions and the net liquid stripping efficiencies for helium are shown in
Table 5. Some minor variation in stripping efficiency with void fraction
was evident at each value of the stripping coefficient. However, the vari-
ations are small enough to be entirely attribdted to precision limits in

the calculations.

Table 5

Comparison of Liquid Stripping Coefficients
And Stripping Efficiencies for Helium

Liquid Stripping Stripping

Coefficient Efficiency
(£t®/hr) (%)

40 7.1 - 7.2

480 47.0 - 47,2
"

 

65

Several intermediate conclusions may be.drawn from the calculations
of helium void fractions in the MSRE: |
1, The calculationaljmodel appears to give reasonable results down
to core void fractions of 0.05 to 0.1 vol. %o
2. For core void fractions below about 0.05%, the neglect of liquid
surface tension effects on the bubbles leads to an underestimate
of the amount ofzgaslthat‘muSt be ingested to establish a given
void fraction. =~
3. For the range of bubble sizes believed to exist in the MSRE
(5 to 20 mils), the effect of bubble size on the void fractions
‘around the loop is small enough'to'be neglected for most purpdses.
4. For the’ekpected values of mass transfer coefficient-betweén
bubbles and liquid (2 to 6.ft/hr), the void fractions in the core
are nearly»ihdepefi&ent*of the mass transfer coefficient.
5. The void fractions around the loop do depend rather heavily on the
amount of liquid stripping that is postulated to occur in the
pump bowl. '

Steady State Xenon Calculations -

_ - A large number of calculations was performed to see if the steady
state xenon poisoning observed in the MSRE could be duplicated by the
| model described in-this report. Of_primary_interestiwere,the variations
witfi.core void fracfiion and the differences between helium and argon cover
gas, These calculations:toOkithe.form,of'parafister'studies in which se-
'_1ectedrparameters were varied, more-or-less srbitrsrily;ito_determine their
lieffects,._As a :esplt_pf;thsssissiculations,1whi¢hipltimate1y reproduced
- the -observed behavior,reasonsbly_Wellj_we vere able to identify some para-
i'fiéters and postulatedmechaqisssfhst appear to bequits;significant in
'ifthe overall description.fls,_ i' " ,'_
. The parameter studies were made by first postulating mechanisms and
lfunctional dependences.of-tyese mechanisms on the core voidif:action. Then
,icalculatians of the xénosquiSoningiwereVmade to see how the,rssults were
affected. Because of the tfial-ahdferfor-nature of this spprosch, many

combinations were tried that added vefy little to the final result. It
 

66
would not further the objective of this report to discuss all of the unsuc- \iij
cessful trials. Bowever, some of these will be described in order to show
the kinds of effects that were obtained. | o '

The first calculations. that were performed assumed an insoluble cover
gas and the results were compared to the reactor experience with argon
cover gas. In the absence of other information, mechanisms and parameter
values were assigned that wefefsimilar to those used in earlier studies.
More specifically, bubble diameters around 10 mils were assumed with low
efficiencies (10% or less) for bubble stripping in the pump bowl. Since
liquid stripping efficiencies in the range of 7 to 15% had been projécted,
‘1iquid stripping coefficients around 160 ft®/hr were used. (These coef-
ficients produced reasonable efficiencies and the effective interfacial
areas required in the pump bowl appeared to be in the right range for the
measured pump-bowl void fractions.) The mass transfer coefficient between
bubbles and salt was set at 4 ft/hr. The only mechanism for transport of
xenon from the circulating fluid to the graphite was assumed to be mass
transfer from the liquid. The mass transfer coefficients of 0.06 ft/hr for
the bulk of the graphite and 0.35 ft/hr for graphite in the central core
region were the same as those recommended by Kedl.'?” No direct ingestion
of clean cover gas into the circulating loop was allowed. All of the
remaining computational parameters were set to the nominal values implied
by the operating conditions and the design of the MSRE.

Figure 17 shows a comparison between the observed xenon poisoning
with argon cover gas and one set of values calculated for an insoluble gas
with the parameters enumerated above.  For these particular calculations,
the reference bubble diameter was fixed at 10 mils for all core void
fractions. The bubble stripping éfficiency was assumed directly propor-
tional to the core void fraction and waé assigned a value of 10% when the
core void fraction was 0.7%Z. The 1liquid stripping coefficient in the pump
bowl varied from 160 ft*/hr at a core void fraction of 0.05% to 186 ft*/hr

at 0.7%; the values were assumed proportional to the fuel pump speed re-
| quired to produce the various void fractions., These results, and others
using slightly modified bubble stripping'efficienciés and liquid stripping
coefficients, indicated that essentially any desired degree of agreement &;,j

e
 

a1 i

LSSSALE R U 1T L LA BB E L 4

67

ORNL=-DWG 71—8040

 

 

 

 

 

XENON POISONING (% 34/4)

 

 

 

 

 

 

 

 

 

0 0 02 03 ©04 05 06  0O7
S CORE VOID FRACTION (%)

Fig. 17. Calculated -a.nd Observed Stéa.dy-State Xenon Poisoning with
Argon Cover Gas — Low Bubble Stripping Efficiency.
 

68

between the observed and calculated poisoning values could be obtained by
"properly selecting" the values of these two parameters. The conclusion
indicated by the results is entirely consistent with earlier conclusions®’
about the variation in xenon poisoning with void fraction when the cover
gas is insoluble. This conclusion is that no special mechanisms, models,
or parameters are required to describe this condition.

There remains, however, one point of difference between these .results
and the overall reactor experience — the bubble stripping efficiencies.
As we indicated earlier, excess bubbles were removed from the MSRE circu-
lating loop with éfficiéncies near 100%. If, as seems reasonable, the
sizes of the circulating bubbles were determined by the action of the pump
impeller, similar stripping efficiencies could be expected to apply to the
xenon calculations., Then, if the bubble-stripping leads to a true exchange
between the circulating bubbles and the cover gas, the stripping effici-
encies required in the calculation are inconsistent with those observed
in the reactor. On the other hand, if the liquid surface in the pump bowl
is covered by a "foam" in which the gas-phase xenon concentration is much
higher than that in the rest of the gas space, the same high rate of bub-
ble exchange would produce a much smaller change in the average-xehon con-
centration in the circulating bubbles. Such an effect would give the ap-
pearance of a low xenon stripping efficiency. The reactor data with argon
cover gas do not allofi us to distinguish between these possibilities.

Since the behavior differences with argon and helium cover gases ap-
peared to offer the best possibility for resolving the xenon behavior in
the reactor, additional calculations were made with loop void fractionms
characteristic of'both‘gases. For the helium cases we used void fractions
obtained for 10-mil bubbles with a gas~to-liquid mass transfer coefficient
of & ft/hr and a pump-bowl liquid stripping coefficient.of 240 ft*/hr. The
xenon and bubble behavior mechanisms were required to follow the same
general patterns for both cover gases.

. Some calculations were performed to see if the two characteristic be-
havior modes could be reproduced by manipulating only the bubble stripping
efficiency and the liquid stripping coefficient. In these.calculatiohs-
the only mechanism for xenon transport to the graphite was, again, mass

transfer from the liquid. Ip general, all of these calculations (for both
 

 

 

69

cover gases) showed the monotonic decrease in steady-state xenon poisoning
with increasing void fraction that was characteristic of the insoluble
cover gas model. Some distortion in this pattern could be obtained by
allowing higher bubble stripping efficiencies at lower helium void frac-
tions but, the large peak in the poisoning curve could not be attained as
long as the bubble stripping efficiency was required to vary as a smooth
function of the void fraction. Figure 18 compares the observed behavior
in the MSRE with the results of one set of calculations in which the bub-
ble stripping efficiency for helium was allowed to vary drastically with
 the core void fraction. The stripping efficiency (superimposed on the
xXenon poisoning plot)-was computed as a constant plus a steeply decaying
exponential., Since the resfilts of this extreme variation failed to even
approach the observed xenon behavior, it seems reasonable to conclude that
the reactor effects were not produced by changes in the stripping effici-
ency alone. 7 |
The results of a large number of calculations indicated that the

mechanism with the greatest capability for affecting the xenon poisoning
at .low void fractions was. the xenon transport to the graphite. This pro-
cess also appeared-capable of producing the differences between helium
and argon with a consistent;treatment of both gases. Accordingly, it was
postulated that xenon transport to the graphite was composed of mass trans-
fer from the liquid-p__; a'contribution from circulatingrbubbles inter-
racting with the walls of the fuel passages. It was evident from the
cover-gas calculations that for a given initial bubble size, the helium
bubbles in the core at low,void fractions would be much smaller than argon -
- bubbles. Thus, if mass transpOrt.by bubble interraction were important
‘and the rate of interraCtion'was_a function of bubble size, the rate of
xenon transport to thergraphite at low void fractions would be much lower
'with helium cover gas than with argon. o
- To test the hypothesis of bubble interraction, a number of calcula-
-tions were made in which the xenon mass transfer coefficient from liquid
to graphite, the rate of bubble interraction with the graphite, and the
bubble- stripping efficiency were all varied, more-or-less independently.

In addition various forms of the functional dependence of bubble interaction
 

70

ORNL~DWG T{—804

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 I i I 100
\ ® OBSERVED XENON POISONING | - g
S 08| 80 5
g &z
© : w
2 \ g
g 06 » 60 i
z o
TN L :
— ., Q.
o
e 04— \ 7 CALCULATED XENON 40 &
z \ POISIONING e
o v
& a0 " 4
-
_STRIPPING EFFICIENCY 2
o l 1 i 0o
0 0Ot ©02 03 04 05 06 O7

- CORE VOID FRACTION (%)

Fig. 18. Calculated and Observed Steady-State Xenon Poisoning with
Helium Cover Gas — Widely Variable Bubble Stripping Efficiency.

 
ulj
:w'

 

71

on bubble size were tried. For each set of calculations, the same cri-
teria for bubble behavior in the loop were applied to both helium and
argon.

As these calculations were being made, it became apparent that some
differences in bubble stripping efficiency between helium and argon would
improve the agreement with the reactor data. The possibility of such a
difference was rationalized on the basis of the liquid behavior in the pump
bowl. Because of the helium solubility, the salt entering the pump bowl
from the loop would contain'more dissolved helium than could be maintained
at the pump-bowl pressure and some outgassing would occur. If this effect
produced a blanket of xenon-rich foam over the salt, the apparent stripping
efficiency for helium bUbbles:wouid be reduced. Since argon was treated as

an insoluble-gas, the effect would apply only to helium. Therefore, lower

 bubble stripping efficiencies were used for helium and the loss in effici-

ency was made a function of the difference between the void fraction in
the salt entering the pump bowl and that in the salt returning to the loop.
(If could be argued that the difference in the helium concentrations in
the liquid streams would be a more logical measure of the degree of gas
blanketing but, the efficiencygreduction is basically arbitrary and any
attempt to define it precisely is unrealistic; the functional dependence
is merely a calculational convenience.)

A somewhat similar rationalization was applied to the liquid stripping
process., It was postulated that the escape of helium from solution in the
pump bowl liquid might enhance_the rate of xenon stripping. Therefore, the

liquid stripping coefficienrs for xenon in helium were allowed to exceed

‘those for argonm. .

 Figure 19 shows the results of a set of calculations in which all of

these factors were included The agreement with the observed steady-state

‘data is. good everywhere except at core void fractions near 0.1% with helium

cover gas, However, the disagreement in this area may be less than is im-
plied by-Fig. 19 because other-reactor data  (cf. Figs. 5 and 6) showed a
more-rapid increase in xenon;poiSOning with increasing void fraction.
Although a reasonablehcorrelation was‘obtained between the calculated
and observed quantities, the parameter values required to produce the cor-

relation were, in some cases, quite different from those that have been
 

72

ORNL~-DWG T71-483

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 | |
et CURVES CALCULATED

<08 A\ POINTS MEASURED |
= _ © HELIUM COVER GAS
; . & ARGON COVER GAS
; 0.6 . - “‘ I
=z \
z .
g 04 / Q\
§ “I o \__
Y 0.2

o

0 o 02 03 04 05 06 07 ,

CORE VOID FRACTION (%)

Fig. 19. Calculated and Observed Steady-State Xenon P01son1ng with
Helium end Argon Cover Gases — Best Fit.
 

73

used previously. ©Some of the more important parameters that were inde-
pendent of the circulating void fraction are listed in Table 6. The ref-
erence bubble diameter and the coefficient for mass transfer between the
bubbles and liquid are within- the range of the'anticipated values. On the
other hand the liquid strippine coefficients led to higher stripping ef-
ficiencies than were predicted’’ and the mass transfer coefficients to
the graphite are lower than the predicted values'’ by a factor of 6. With
argon cover gas, the apparentrliquid stripping efficiency varied from 17%
at the lowest core fractions to about 38% at a core void fraction of 0.6%.
With helium cover gas, this efficiency was about: 30% and essentially inde-
pendent of the core void fraction. These values are probably close enough
to the expected efficiencles to be credible. The discrepancy in the mass
transfer coefficient is considerably greater than the usual uncertainty

in predicting such quantities'and there is no basis for adopting the lower
value except that it appears to permit'better correlation of the observed
results. There is, however, some basis for expecting somewhat lower

| liquid-graphite mass transfer in the MSRE than would be. predicted in other
systems. | | _

The mass transfer process was described in the calculations as a pro-
duct of the coefficient and a driving potential based on xenon concentra-
tions in the salt and graphite. The internal heat generation in the fuel
and the laminar flow conditions in most of the core resulted in a tempera-
ture distribution in the salt®® in each channel such that the lowest tem-

perature was at the center of the channel, Since xenon has atlarge posi-

'_rtive temperature coefficient of solubility in salt the liquid immediately

| adjacent to the graphite would have a higher xenon solubility than the
- rest of the liquid and the higher solubility would tend to reduce the
’driving froce for xenon transfer into ‘the graphite. This effect was not
__examined in detail but it does not appear to be large enough to account
-"for all of the difference between the originally predicted transfer rate
fand that required to match the observed steady-state poisoning.
B - In addition to the parameters just described the bubble stripping

"ffefficiencies and the rates of bubble interaction with the core graphite

were deliberately varied with void fraction in the calculations. Figure 20

shows graphically the values that were used to produce the xenon poisoning
 

 

74

Table 6

Constant Parameter Values Used to Correlate
Calculated and Observed Steady-State Xenon
Poisoning in MSRE

Parameter Value

 

 

Argon "Helium
Cover Gas Cover Gas
Reference bubble diameter (mils) 10 | 10
Mass Transfer Coefficient (ft/hr) -
Bubbles~to-Liquid — 4 | 4
Liquid—to—graphite'ih most ' :
graphite _ 0.01 0.01
Liquid-to-graphite in central '
core region ‘ 0.063 0.063
Pump bowl liquid stripping - . |
coefficient (ft*/hr) - 100 240

 

results of Fig. 19. The bubble strippifig efficiency for argon was computed
as a linear function of the total void fraction ingested into the circu-
lating loop from the pump bowl. Because of the insoluble gas treatment

for argon, the void fraction at any point in the fuel loop is also a linear
function of the ingested void ffaction and the plot of stripping efficiency
against core void fraction is a straight line. The same linear function of
ingested void fraction was used as a basis for the helium bubble stripping
efficiencies but the individual qfiantities were reduced to-from 36 to 61%
of their nominal values to account for the postulated gas blanketing of the
pump-bowi liquid. Whefi the results are plotted against the core void frac-
tidfi,,a (nonuni form) translation toward the abscissa occurs_which distorts
the curve to the shape shown in Fig. 20. The nominal rate of bubble inter-

action was chosen (by an iterative process of empirical optimization) to
 

 

75

ORNL—DWG 74-8042

03 /,/
- ARG% /

 

04

 

 

02 . | /,
_ / / &EL!UM

 

oA

N\

 

BUBBLE INTERACTION RATE (liters/min)

 

100

80 - — L /
' | | - arcon

60 —— : /
40 - ' // — /H/ELIUM
"’ / ; -
0 : : : :

c o4 02 03 04 05 06 OF
'CORE VOID FRACTION

 

 

 

 

 

BUBBLE STRIPPING EFFICIENCY (%)

 

 

 

 

 

 

 

 

 

Fig. 20 Parameter Values Used in Xenon_Calqu.ajtions for Best Fit.
 

76

cause 1.14%Z of the bubbles with a diameter of 8.4 mils to collide with the -
walls of the fuel channels. (An insoluble gas bubble whose diameter is
10 mils in the pump bowl has a diameter of 8.4 mils at the core pressure.)
The bubble collision probability was also assumed to vary linearly with
bubble volume. Thus, for argon cover gas, the fraétion of bubbles inter-
acting with the graphite was independent of the wvoid fraction and the total
rate of gas flow became a linear function of core void fraction,i For
helium, where dissolution has a significant effect on bubble size, the gas
flow rate to the graphite is lower at low and intermediate void fractions.
It is clear from the results §hown in Fig. 19 that xenon transport
to the graphite from the bubbles had a major effect on the net xenon poi-
soning that was calculated. The magnitude of this effect was examined in
a series of calculations in which only that one parametet,was changed.
Figures 21 and 22 show, for helium and argon cover gas, respectively, the
poisoning that was obtained when xenon transport from bubbles directly to -
the graphite was eliminated from the previous calculations. In each figure,
the appropriate curve from Fig. 19 is reproduced to ptovide.a direct com-
parison. These results show that,'except at very low helium:void fractions,
most of the poisoning was due to xenon transported to the graphite by
bubbles. |

In addition to providing information about the net xenon poisoning,
the steady state calculations indicated the relative distribution of that
poisoning among the gas bubbles, liquid, and graphite in the reactor core.
This distribution, as we will show later, has a significant effeét on the
xenon transient behavior, especially for xenon removal transients.

Figure 23 compares the fraction of the total xenon poisoning due to xenon
in the graphite for the two sets of system parameters used to calculate

the steady-state results shown for argon cover gas in Figs. 17 and 19.
Although both sets of calculations reproduced the observed results reason-
ably well, the first set (Fig. 17) allowed only Xenon mass transfer from
the liquid to the graphite and required low bubble stripping efficiencies
whilejthe second set (Fig. 19) allowed bubble interaction with the graphite
and required higher bubble stripping efficiencies. Both calculations re-
sulted in about the same xenon distribution at low void fractions but the
bubble interaction mechanism led to much higher contributions from the

graphite at the higher void fractioms.
77

ORNL-DWG T71-8043

 

 

 

 

 

 

 

 

10
- .
SoslD
52 '\ _LIQUID AND BUBBLE
= TRANSPORT
Q A
Z06 :
Z \
A
o
% 04
- o2l : : '
N\JLIQUID TRANSPORT
ONLY
o |

 

 

 

 

 

 

 

0 0.1 0.2 0.3 04 05 0.6 o7
' CORE VOID FRACTION (%)

Fig. 21. Effect of Xenon Transport to Graphite by Helium Bubbles.

 

 

 

  
 

78

ORNL-OWG M-8044

 

8

 

 

==t~ LIQUID AND BUBBLE TRANSPORT

VERRS

LiQUID TRANSPOR}' ONLY
: i

0.1 02 03 04 05 0.6 07
CORE VOID FRACTION (%)

o
o

 

p -

 

o
n

 

 

 

XENON POISONING (% 34/%)
o
s

 

 

 

 

 

 

 

 

o

 

Q

 

Fig. 22. Effect of Xenon Transport to Graphite by Argon Bubbles.

 

 
 

79

ORNL-DWG T1-8045

] i l ]
WITH BUBBLE INTERACTION

 

o

 

\\
\
\\

NO BUBBLE INTERACTION ™

 

o
o

 

o
N

 

o
N

 

o
0

 

 

 

 

 

 

 

 

 

FRACTION OF XENON POISONING IN GRAPHITE

o .
o

of ©02z 03 04 O5 06 O
CORE VOID FRACTION (%)

Fig. 23. Effect oerendn'Transport by Bubbles on Core Xenon Distri-
bution. . '
 

 

80

Although the principal objective of these calculations was to see what
mechanisms and parameter values could produce.xenon poisoning results like
those observed in the reactor, some information was also gained about the
effects of other parameters. In the discussion of bubble stripping it was
noted that two extreme behavior modes could be assumed for the gas that
was added to unstripped bubbles to restore their ofiginal sizes prior to
reingestion, At one extreme was the assumption that the unstripped bubbles
are restored by agglomeration so that the additional gas was characterized
by the average xenon concentration in the pump~bowl gas space. This as-
sumption appeared to be the least controversial so it was used for most
of the Computations, including those which prdducéd the results shown in
Fig. 19. At the other extreme was an assumption that the additional gas
required was clean helium. The effect of the latter assumption was exam-
ined by applying it to the calculations for helium cover gas just described.
Figure 24 shows a comparison of the two sets of xenon poisoning results.
Also shown on this figure is the absolute rate of clean helium ingestion
(at pump-bowl temperature and pressure) that resulted from the assumed
behavior. It is clear from these results that the rate of ingestion of
clean helium at the pump suction, either directly or by growth of un-
stripped bubbles, could have been manipulated in the calculational model
to significantly modify the values of other parameters needed to match the
observed xenon behavior. However, it did not appear that the ingestion
of cover gas alone could produce the major difference between helium and
argon.

Earlier in this report we indicated that some ambiguities still exist
in the nuclear data for xenon. For purposes of this study the most sig-
nificant questions were the direct yield of '®°Xe from fission of *3*°U and
the neutron absorption cross section of *®*MXe. Although neither of these
quantities was expected to have a large effect on the steady-state xenon
poisoning, some calculations were performed to see what the effects might
be. Two values were selected for the direct yield of '®°Xe: 187 and 3.6%,
respectively of the total yield (6.16%) from 232U fission. Since the cal-
culational model neglected the neutron cross section of '*°™Xe, the effect

of this cross section was simulated by adjusting the branching ratio for
 

 

 

81

 

 

ORNL-DWG T1-8046

 

)8
/

 

 

 

g INGESTION RATE
~
% 04 OF CLEAN HELIUM
e \
& 02 ]
§ |
0
08

 

\
/

 

 

~
] A1 =
T ~——

CLEAN HELIUM INGESTED

/ "w CLEAN HELIUM

 

 

 

 

 

XENON POISONING (% 84/4)
N H

 

 

 

 

 

 

 

o o4 0.2 03 C4 05 06 o7
CORE VOID FRACTION (%)

Fig. 24, Effect of Clean Cover-Gas Ingestion on Steady-State Xenon
Poisoning, Helium Cover Gas. '

.

-

 

 

 
 

82

1357 decays to '*°Xe and '®°mXe. Table 7 compares the results that were
obtained for one set of bubble parameters. Although the parameters used
to describe the physical processes in the reactor were not precisely the
same as those discussed earlier, the relative effects of the nuclear pro-
perties would not be expected to change. It is clear from these results
that the lack of precise nuclear data for the 135-mass chain has an insig-
nificant effect on the description of the steady-state xenon poisoning.
One of the approaches that has been suggested for reducing the xenon
poisoning in molten salt reactors is the development of a graphite with a -
substantially greater resistance to xenon diffusion than that used in the
MSRE. Since it was easy to vary this parameter in the steady-state calcu-
lations, some results were produced to evaluate the importance of the
xenon diffusion coefficient in graphite. These results also showed the
effect of uncertainties in this parameter on the calculated xenon behavior
in the MSRE. The diffusion coefficient for xenon appears in two general
areas in the mathematical model: in the deScription of xenon migration
between the major graphite regions in the core and in the description of
the radial xenon profile within individual moderator pieces. Because of
the low order of importance of the first process; only the effects in the
moderator pieces were examined. Xenon poisoning calculations were made as
a function of the void fraction of bubbles in the core for several values
of the xenon diffusion coefficient in graphite ranging down to 10~7 ft?*/hr
(2.6 x 10™® cm?®/sec). The results at each void fraction were then normal-
ized to values obtained for a flat xenon profile (infinite diffusion coef-
ficient) in the moderator pieces. The xenon poisoning, relative to the
normalization standard, is shown as a function of diffusion coefficient
in Fig. 25 for helium cover gas. (The results with argon cover gas were
essentially the same.) The range of values at each diffusion coefficient
reflects the influence of xenon stripping, withhthe upper end of the range
corresponding to low core void fractions or relatively poor xenon stripping.
Thus, for poor stripping, the graphite diffuéivity must be very low to pre-
vent xenon fransport to the moderator. On the other hand, if an efficient
xenon étripping process is available, it can compete effectively with gra-

phite that has a much higher diffusivity.

8
 

 

83

Table 7

Effect of **®Xe Nuclear Properties on

Steady State Xenon Poisoning

Fraction of Total !*°Xe
Yield Produced Directly

Fraction of **°I
Decays that

Calculated
Steady State

- Xenon Reactivity

 

From 2°°U Fissgion ~ Produce !3°T%e ~ Effect
(%) (%) (% 8k/k)
* *
18 - 30 -0.276
3.6 30 -0.275
18 -0,280
3.6 —0.279

 

%
Nominal wvalue.

Diffusion qoefficiefité.fbr'hélium at 23°C have been reported®® for

several samples of MSRE graphite.-

These values, when converted to xenon

at 1200°F give diffusion coefficients that range from 3 x 1077 to
2 x 10~ ft?/hr for surface samples and from 1 x 10™% to 9 x 107" ft*/hr
for interior samples. The averages of 20 samples are 2.3 x 10™® ft?/hr

for surface material and 1.3 x 10—* ft’/hr for interior material. Within

- -this range, the value used for the graphite diffusion coefficient has lit-

tle effect on the calculéted'stéady-State xenon poisoning. Nevertheless,

the results discussed above include the effect of the xenon distribution

lations.

~in the graphite.' However, we did not include it in the transient calcu-
 

 

 

84

ORNL—DWG 71-8047

 

 

 

 

 

RELATIVE XENON POISONING

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
5 w2 5 ©%2 5 w2 s w2
GRAPHITE DIFFUSION COEFFICIENT (£t2%/hr)

Fig. 25. Effect of Graphite Diffusion Coefficient on Steady-State
Xenon Poisoning, Helium Cover Gas.

"
 

 

85

Transient Xenon Calculations

In addition to satisfactorily describing the steady-state xenon poi-
soning in the reactor, a model that represents the actual physical pro-
cesses correctly should also describe the transient behavior that follows
a change in reactor power level., The preceding discussion of the steady-
state calculations shows that, for at least some situations, significantly
different combinations of parameter values and mechanisms produced com-
parable overall results, but the inclusion of direct xenon transport from
bubbles to the graphite produced a significant difference in the xenon
distribution at high core void fractions. In an effort to evaluate this
mechanism and other parameter-values,.some transient calculations were
performed. Ideally, if a sufficient variety of reactor xenon transients
were available for compafisqn and if the various models were sufficiently
flexible, it should be possible to deduce mechanisms and parameter values
that satisfy all conditions. However, only a fefi xenon transients were
recorded for the reactor under a‘limited variety of conditions. 1In ad-
dition, the calculatien'of’e'large number of transients for different in-
put parameters was impractieal. As a censequence, we did not succeed in
clearly identifying all the'mechanisms and“parameters required to match
the MSRE experience. Howe#er, the»calculatione did 11lustrate some im-
portant features of the xenon behavior and showed some of the deficiencies
of the postulated mechanisms.

The transient most commonly encountered in the reactor operation was

the buildup of the xenon poisdfiing following-a rapid increase in reactor
_power from near zero to several megawatts. The controlling parameters

~in such a transient appearfiieibe the half-lives of the iodine and xenon

'and;the'kenon burnupfcdefficient.:'Consequently, this type of transient is

relatively insensitive to variations in the parameters that were of in-

- terest in this study. In addition, the parameters that were considered

in the steady-state anelyées'pfodnced comparable xenon distributions as

well as-comparable-poisbning effects at low core void fractibns. Conse-

quently, we did not calculate any xenon buildup transients at low void
fractions; other types of transients seemed more likely to show differences

due to the choice of parameters. Figure 26 shows the first 40 hr of a
 

86

ORNL-DWG 71-8048

=™
N

P
o

o
w

o
>

e
i

  

FRACTION OF FINAL STEADY-STATE VALUE
) o
Q. o

8 12 6 20 24 28 32 36 40
TIME AFTER POWER CHANGE (hr)

o
H

- Fig. 26, Comparison of Calculated and Observed Xenon Buildup Tran-
sients in MSRE, Helium Cover Gas with 0.53 vol % Voids in Core.

( |
. ‘-’
"
 

 

87

xenon buildup transient following_a rapid increase in reactor power from
10 kw to 5.5 Mw with helium cover gas and a core void fraction of about
0.53 vol 7. Also shown are two calculated transients for different para-
meter values. (Since the calculations did not lead to precisely the same
steady-state values, the data for the transients were normalized to their
regspective steady-state values to emphasize the shapes of the curves.)
For one. of the calculations (dashed curve) no direct xenon transport from
bubbles to graphite was allowed and the nominal coefficient for xenon mass
transfer from liquid to graphite was used — 0.06 ft/hr in the major core
regions. These parameters required a bubble stripping efficiency of 47%
and-showed 0.57 of the total xenon poisoning in the graphite at steady
state. For the second calculation, 0.94% of the gas flowing through the
core was allowed to interact with the graphite and the coefficient for
Xenon mass transfer from liquid-to graphite was reduced by a factor of 6.
This led to a bubble stripping efficiency of 61% with 0.95 of the total
xenon poisoning in the graphite. These parameters are similar to those
used to calculate the steady-state poisoning shown in Fig. 19. The dif-
ferences in the calculated transients are quite small and neither rises
as rapidly as the observed transient.

% it appeared

From previous studies of,xenon.transients'in the MSRE,
that better discrimination could be obtained with xenon removal transients.
Therefore, two sets of removal'transients were computed for parameter
values that produced highépower, steady-state results close. to those ob-
served in the reactor. 'For°one'set,'Figure 27, the caleulations were com-
pared'tO-a reactor transient obsetved after a shutdown from 5.5 Mw to 10 kw

with helium cover gas and a core void fraction of 0. 53 vol Z. The para-

., meter values for the calculations, both with and without bubble interaction

 

were the same as those described ~above for the buildup transient. The re-
sults are again normalized to. their reSpective steady-state values at the
‘high power level. - _ |

Both of the calculated .curves show a peak in the xenon poisoning af-
ter the power reduction. This peak'is'associated with the continued pro-
duction of '®°Xe by decay of '*°I in the salt and the transport of that
xenon to the graphite. Thus, as the graphite contribution to the total
 

88

ORNL-DWG 71-8049

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
S T T T T 11
10 =\ J-CALCULATED WITH BUBBLE INTERACTION
;-‘-'l *e . ‘\
< I
=~ 4
m B
> 08 | . =
Q ~
< . ~
£ o6 . S,
o . N —CALCULATED WITH NO
2 | < BUBBLE INTERACTION
E 04 *a -
= <<
=z b ~
5., OBSERVED™" oINS~
v B o
5 se®| o \"-:.
= ? *eyq. 4
g o it
E 0 4 8 {2 % 20 24 28 32 36 40

TIME AFTER POWER CHANGE (hr)

Fig. 27. |Comparison of Calculated and Observed Xenon Removal Tran-
sients, Helium Cover Gas with 0.53 vol % Voids in Core.

 
 

 

89

xenon poisoning increases, this peak tends to increase, both in magnitude
and duration. This seems to suggest that parameters which allow very poor
xenon transport to the graphite at high void fractions, and thereby attri-
bute most of the poisoning to xenon in the circulating fluid, mightrbetter
describe the transient behavior.' However, such parameters also require
very low stripping rates to describe the steady-state poisoning and these
stripping rates produced transients that were much slower than those ob-
'served in the reactor. This is illustrated by the more "stretched out"
shape of the transient in which no bubble interaction with the graphite

was allowed. It was also noted that faster rates of exchange between xenon
in the graphite and that in the fluid tended to reduce the peak in the poi-
soning curve. In these cases, however, the stripping efficiencies required
to match the steady-state results were so high that the rate of decrease

of the poisoning after the peak was considerably faster than was observed
in the reactor. '

The'second'cOmparison hetween calculated and observed xenon removal
transients, Fig. 28, was made for a reactor test in which the cover gas
was argon and the core void fraction was about 0.7 vol %Z. When no bubble
interaction was allowed- the xenon parameters used were the same as those
that produced the correlation shown in. Fig. 17; 10% for the bubble strip-
ping efficiency and 0.06 ft/hr for the Xenon mass transfer coefficient
from liquid to graphite. With bubble interaction‘the Xenon parameters
were the same as those used:for Fig. 19. The calculated curves show many
of the same featnresias;those in Fig. 27. In this_case, however, when no
; bnbble interaction was allowed,'thehpoisoning contribution.from xenon in
- the graphite was small enough'that the peak in the curve was completely
eliminated. This curve also shows the very slow removal of xenon that
was- projected for this condition. 'When bubble interaction with the graph-
ite was added, the poisoning peak_reappeared because the_overall xenon
distribution was again shifted:tOWard the graphite. Once the peak was
passed, the higher stripping_efficiency used in that_calculation produced
'”a'ratecof'xenon.removalathat_wasclose to the observed rate.

In addition to the computations to examine the effects of the xenon

transport parameters on the transient behavior, some calculations were
 

90

ORNL-DWG 71-8050

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g 1.2 1 1 I T T T T
§ CALCULATED WITH BUBBLE INTERACTION
K40 & 3'\4:(\
g ~
) ®* L
)
" 06 s . \\ <
4 T° ~ -CALCULATED WITH NO
Eoa OBSERVED—"" 1 - \B‘liBBLE INTERACTION _
Z . .
& ‘1. ~d_
g o2 - ~=
- s 4 e
§ 0 T
E 0 4 8 12 #®© 20 24 28 32 36 40

TIME AFTER POWER CHANGE (hr)

Fig. 28. Comparison of Calculated and Observed Xenon Removal Tran-
sients, Argon Cover Gas with 0.7 vol % Voids in Core.
 

 

 

 

91

performed to study the effects of the direct xenon yield and decay scheme.
The xenon tramnsport parameters for these calculations were very similar to
those used for the transients with argon cover gas and bubble interaction
with the graphite. However, the rate of bubble flow to the graphite was
lower by a factor of 2.3 in these calculations. Figure 29 compares a
xenon removal transient using the nominal direct yield of '*°Xe (18% of
total) with one in which only 3.6% of the xenon yield came directly from
fission. (Changing the branching ratio for *®°I decay to simulate a high
cross section for '®3MXe had essentially no effect on the shape of the
transient.) The higher peak in the transient curve for the lower direct
yield results from the higher rate of *2°Xe production after the power
reduction and the migration of some of that xenon into the graphite. The
higher peak in the nominal curve, relative to the comparable curve in

Fig. 28 reflects the lower rate of exchange between xenon in the graphite
and that in the fluid. That is, the xenon in the graphite stays there

longer. and so delays the influence of the stripping parameters.

DISCUSSION OF RESULTS

In the studies reported here we have examined the effects of a number
of system parameters on the calculated behavior of '®°Xe in the MSRE. The
goal of this effort was to see if the behavior observed during reactor
“operation could be predicted by a model that included the effects of cover-
gas solubility in the fuel salt with reasonable values for otherrparameters.
Significant deviations from the nominally predicted xenon stripping and
mass transfer effects were postulated in an effort to reproduce the dif-~

'ferences in xenon poisoning that were observed with soluble and insoluble
 cover, gases. Although we. achieved reasonable success in describing the
steady-state xenon poisoning with both helium and argon cover gas, we
could not adequately describe the transient behavior. The nature of the
- various results that Were'obtained'provides some insight into the kinds
of processes that may'haverbeen-important\in the MSRE.

The calculations using previously accepted transport mechanisms and

parameter values showed again that the steady-state results with argon
 

92

ORNL-DWG T1=-8051

 

 

 

 

 

 

g 10 \&

§ \ DIRECT YIELD =3.6% OF TOTAL
S o8 AN

& N

2 o6 N

W | \\

w N

g 04 DIRECT YIELD = 18% OF TOTAL ™

q =

g 02 \\‘
o \§

 

 

 

 

 

 

 

 

 

 

 

 

0
O 4q 8 2 € 20 24 28 32 36 40

TIME AFTER POWER CHANGE (hr)

Fig. 29. Effect of Direct 135ye Yield on Xenon Poisoning Transient.
 

 

 

93

cover gas could be readily. duplicated. However, such calculations re-
quired the use of bubble stripping efficiencies that were much lower than
the bubble removal rates that were observed in the reactor when excess
bubbles were present. It is, of course, conceivable that the bubble strip-
ping efficiency for xenon might be much lower than the rate at which a new
void distribution is approached. This would be the case if, for example,
stripped bubbles were replaced by bubbles containing an abnormally high

xenon  concentration because of the existence of a "foam" blanket on the

~salt surfece in the pump. There is evidence from observations in the pump

bowl that some kind of foam layer was indeed present;*' however, its char-
acteristics are not well defined and any conclusions about its effect on
the xenon behavior would be-highly\speculative. .When the low stripping
rates required for these steady-state results were applied to transient.
caiculations,with high argon.void fractions, they produced decreases in
the xenon poisoning that were much slower than those observed in the re-
actor after power reductions. The transient response for a given strip-
ping efficiency would have been faster if a larger fraction of the total
xenon poisoning had been . associated with the circulating fluid; i.e. less
xenon in the graphite. This condition would be favored by a lower coef-

ficient for xenon mass transfet ftom the liquid to the graphite;‘ However,

.such a shift would require still lower stripping efficienies to describe

the steady-state results. Thus, it appears that xenon transport rates to
graphite and stripping efficiencies like those .used in earlier analyses
could not describe the transient behavior at high void fractions, even for
an insoluble cover .gas. C ) i”, , |

' - One conceivable way in which the original parameter values could be
made to_approach thenobserved;results,at high void fractions would be to

make the.etripping effiCiency.dependent-On_the reactor_powef level. If

- the stripping efficiency wereiextremelyulow with the reactor at power (and
lthe rate of mass transfer to the graphite were also lower than predicted)
most of the xenon poisoning would be assoclated with the fluid and the
-.poisoning wouid build up;rapidly to its,steadyfistate value. Then, if

‘higher stripping rates preveiled'at,very low powers, rapid removal of the

xenon-would result, This hypothetical situation might be achieved if some
short-lived material were present in the salt that had the capability of
 

 

 

94

- holding xenon in the fluid in such a way as to make it unavailabie for
stripping or transport to the graphite. Since there appeared to be no
firm basis for postulating the condition just described, this approach
was not pursued in the xenon analysis.

Even if power-dependent changes in stripping efficiency were postu-
lated to explain the total xenon behavior at high argon void fractionms,
we found that we could not describe the poisoning that was observed with
helium cover gas. Inclusion of the helium solubility effects and wide
‘variations in,xenonlétripping as a function of void fraction modified the
calculated poisoning but we could not match- the observed results. It ap-
peared that some process of variable xenofi transpbrtzto the graphite, in
addition to the relatively constant mass transfer from the liquid, would
most -likely be .capable of describing the observed effects of circulating
voids on the xenon poisoning. The requirements on this process were that
it contribute very little to the total xenon poisoning wheh the gas bub-
bles in the core Saltfwere'small and substantially more when larger bub-
bles were present at the same void fraction. Incorporation of an addi-
tional transport mechanism with this property, along with a reduction in
the coefficient for xenon mass transfer from the liquid to graphite made
it possible to describe the steady-state poisoning with both helium and
argon cover gas in one self-consistent approach. The poisoning difference
between the two cover gases at low void fractions resulted from lower
-xénon transport to the graphite from helium bubbles which were reduced in
size by dissolution in the salt. (Xenon transport to the graphite may not
be the only process that could produce this difference but the graphite
appeared to offer the only reservoir with sufficient xenon storage capa-
bility to account for high poisoning levels that were observed with argon
at low void fractions.) In this study we described the additional xenon:
transport process in terms of interaction of gas bubbles with thelgfaphite
mass. Actual collision of bubbles with the walls is physically unrealistic
but other mechanisms that involve bubble nucleation:on'the walls®® have

been suggested that are physically more palatable and would have the same

C
 

 

 

95

net result, Furthermore, there is some evidence in the MSRE experience
that gas bubbles did tend to collect on core surfaces.*

Although the use of a bubble transport process for xenon led to a
better description of the steady-state poisoning as a function of void
fraction, it did not produce,satisfactory transient resultsgat high void.
fractions. The transients indicat'ed that this approach ;i:ended to shift
the xenon distribution too muchftOWard the graphite. ‘Better agreement
could have been obtained if. the bubble transport process had become rela-
tively less effective at the higher void fractions. However, this possi-
bility was not pursued'in'the‘analysis. - |

CONCLUSIONS |

The ‘successful, extended operation of the MSRE provided a valuable
demonstration of the operating characteristics of a molten-salt reactor.
One of the more advantageous of these characteristics-is ‘the ability to
effectively remove noble-gas fission products *'notably 135%7¢ — with rela-
tively little effort. This removal reduces the total inventory of fission
products in the primary loop and also the reactivity loss to 3°Xe poi-
"soning. Depending”on the'cover gas:and'the volume fraction of circulating
voids that were maintained in the fuel loop, the xenon poisoning in the
MSRE was reduced by a factor of 2 to 6 below the values that would have
prevailed with no gas stripping. '

| Although some aspects of the xenon behavior (e.g. strong ‘dependence
lon'circulating.void fraction)“were-expected, the reactor results showed
‘that the total behaviOr vas:nof'accurately‘predicted | In'particular; the
sensitivity of the xenon poisoning to the choice of cover gas had not been

l'predicted. Subsequent analyses of the operating results were partially

 

] *The power disturbances ("blips“)as observed in the reactor apparent-

ly occurred when small amounts of gas that had accumulated in the core
were swept out. In addition, during an experiment in which the fuel was
circulated by natural circulation, the presence of a positive pressure
coefficient of reactivity implied the presence of gas in core locations
where it was subject to compression by salt. :
96

successful in describing the observed xenon behavior but also revealed
some areas of continuing uncertainty. We found that solubility effects
were important with helium cover,gas but that these effects alone appar-
ently could not explain the xenon poisoning differences between helium and
argon at low core void fractions. . In attempting to describe the reactor
results we found it necessary to postulate bubble and liquid stripping ef-
ficiencies in the pump bowl that were substantially higher than predicted
values and liquid-to-graphite mass transfer coefficients that were much
lower. In addition it appeared that circulating voids strongly influenced
the rate of xenon mass transport to the graphite in a way that depended on
both the bubble fraction and bubble size. It also appeared that some argu-
ment could be made for changes in stripping efficiency with reactor power
leyel. The differences between predicted parameter values and those pos-
'tulated in this study suggest that additional effort to deyelop a better
quantitative understanding of bubble effects in mass transport and gas
stripping would be of value.

Since the good breeding performance of conceptual designs of large
molten—salt reactors depends on effective 13%%e removal, the ‘ability to
accurately predict xenon poisoning is important in the design and evalu-
ation of future reactors. Some of the questions raised by the MSRE study
for which accurate and reliable answers would be useful in making such pre-
dictions are the following: |

1. What are the solubility characteristics of various fission-
product gases and cover gases in potential molten-salt fuel mixtures?

2. How and to what extent do circulating bubbles affect the mass
transport of xenon from the fluid to graphite? What is the effect of bub-
ble size on this process?

3. What is the effect of heat generation in the fluid on mass trans-
fer to graphite?

4; What are the effective rates of xenon mass transfer from liquid
salt to;circulating_bubbles and how are these influenced by dissolution and
evolution of cover g387

3. Is there any basis for expecting an effect of power level on

Xenon removal e.g. through generation of materials that affect the gas

‘transport. processes?
 

 

97

- ACKNOWLEDGMENT

The assistance provided by R. J. Kedl in the formulation of the
mathematical descripfions; in the provision of parameter values, and in

reviewing the manuscript is gratefully acknowledgéd.
 

1.

9.

10.

11,

12,

13.

14,

98

'REFERENCES

R. C. Robertson, MSRE Design and Operations Report, Part I,
Description of Reactor Design, ORNL~TM-728, (January 1965).

P. N. Haubenreich, 'Molten Salt Reactor Progress," Nucl. Eng.
Int'l.,, 14 (155): pp. 325-329, (April 1969).

P. N. Haubenreich and M. W. Rosenthal, "Molten Salt Reéétors,"
Science Journal, 5 (6): pp. 41—%6, (June 1969).

Paul N. Haubenreich and J. R. Engel' “Expefiencé with the Molten-
Salt Reactor Experiment," Nucl. Appl. & Tech., 8 (2) pp. 118-136,
(Feb. 1970).

A. Houtzeel and F. F. Dyer, A Study of Fission Products in the Molten
Salt Reactor Experiment by Gamma Spectrometry, ORNL-TM-3151, in
preparation. '

Reactor Chemistry Division Ann. Progr. Rept., Dec. 31, 1965,
ORNL-3913, pp. 3840.

M. K. Drake, National Neutron Cross Section Center, Brookhaven
National Laboratory, personal communication to J. R. Engel,
Nov. 19, 1970.

L. L. Bennett, Recommended Fission Product Chains for Use in Reaptor
Evaluation Studies, ORNL-TM-1658 (Sept. 26, 1966).

C. B. Bigham, A. Okazaki, and W. H. Walker, "The Direct Yield of
Xe-135 in the Fission of U-~233, U-235, Pu-239, and Pu-241," Trans.
Am, Nuc. Soc. 8 (1): p. 11 (June 1965).

W. D. Burch, Measurement of Xenon Poisoning in the HRT, ORNL-TM-228
(April 19, 1962).

P. G. Smith, Water Test Development of the Fuel Pump for the MSRE,
ORNL-TM-79 . (March 27, 1962).

P. G. Smith, Development of Fuel- and Coolant-Salt Centrifugal Pumps
for the Molten Salt Reactor Experiment, ORNL-TM-2987 (October 1970).

J. R. Waggoner and F, N. Peebles, Stripping Rates of Carbon Dioxide
from Water in Spray Type Liquid-Gas Contactors, EM 65—3-1 University
of Tennessee (Thesis), (March 1965).

MSR Program Semiann, Progr. Rept., Jan. 31, 1963, ORNL-3419, pp. 27-28.
 

 

 

15.

16.

17.

18.

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21.
22,

23.

24,

25,

26,

- 27,

28,

29,

130,

99

MSR Program. Semiann._Progr. Rept., July 31, 1964, ORNL-3708,
PP. 373—389

MSR Program Semiann, Progr. Rept., Feb. 28, 1965, ORNL-3812,
pp. 76-80,

R. J. Kedl and A. Houtzeel, Development of a Model for Computing
'*%%e Migration in the MSRE, ORNL-4069, (June 1967).

MSR Program Semiann. Progr. Rept., Aug. 31 1965, ORNL-3872,
pp. 22—23

J. Re Engel -and - B, E.;Prince, The- Reactivity Balance in the MSRE,
0RNL-TM-1796, (March 10, 1967)

B. E Prince, J. R. Engel and C, H, Gabbard Reactivity Balance
Calculations and Long Term Reactivity Behavior with 2°%U in the MSRE,
RNL—4674 (in preparation)

J. R. Engel P. N. Haubenreich and A, Houtzeel, Spray, Mist, Bubbles,
and Foam in the Molten Salt Reactor Experiment ORNL-TM—3027 (June 1970).

MSR Program Semiann. Progr._Rept., Aug. 31, 1966 ORNL-4037,
pp. 22-24. -

MSR Program Semiann. Progr. Rept., Feb 28 1967 ORNL-4119,
pp. 17-18.

J. C. Robinson and D.'N;'Fry; Determination of the Void Fraction in the
MSRE Using Small Induced Pressure Perturbations, ORNL-TM-2318-
(Feb 6, 1969). R |

MSR Program Semiann. Progr. Rept., Feb. 29, 1968 0RNL—4254 pp. 4—6.

D. N. Fry, R. C. Kryter, and J. C. Robinson, Measurement of Helium
Void Fraction in the MSRE Fuel Salt Using Neutron-Noise Analysis,

ORNL-TM~-2315, (Aug. 27, 1968)

'R. J. Kedl, The Migration of a Class of Fission Products (Noble Metals)

in the MSRE, ORNL-TM Report, in preparation.

1MSR Program Semiann. Progr.,Rept., Feb. 28, 1969 0RNL—4396

C. H. Gabbard, ReactorrPowerfMeasnrement and Heat Transfer Performance
in the Molten-Salt Reactor Experiment, -0RNL-TM#3002 (May, 1970).

MSR Program. Semiann. Progr. Rept., Feb. 28, 1970, ORNL—4548

pp. 6566,
 

 

31.

32.

33,

34.

35.

36.

37.

38.

39.

40.

41,

100

MSR Program Semiann. Progr. Rept., Aug. 31, 1969 ORNL-4449,
pp. 10-11. .

MSR Program Semiann. Progr. Rept., Aug. 31, 1970 0RNL—4622
PP. 2.

MSR Program Semiann. Progr. Rept., Aug. 31, 1967 0RNL—4191
pp. 55-58.

B. E. Prince, personal communication to R. C. Steffy, April 25, 1969.

S. J. Ball and T. W. Kerlin,. Stability Analysis of the Molten Salt
Reactor Experiment, ORNL-TM-1070, p. 68, (December 1965).

S. J. Ball and R. K. Adams, /MATEXP°/VA'General Purpose Digital
Computer Program for Solving Ordinary Differential Equations by the
Matrix Exponential Method, 0RNL—TM—1933, (August - 30, 1967)¢-

MSR Program Semiann. Progr. Rept., Feb 28, 1970, ORNL-4548,
PP. 37-38. , ,

J. R. Engel and P. N. Haubenreich, Temperatures in the MSRE Core
During Steady-State Power Operation, ORNL-TM-378, (Nov. 5, 1962).

R. B. Evans 111, J. L. Rutherford, and A. P. Malinauékas, Gas Trans-
port in MSRE Moderator Graphite, II Effects of Impregnation,

- II1 Variation of Flow Properties, ORNL-4389, p. 52, (May 1969).

MSR Program Semiann. Progr. Rept., Feb, 28, 1967, 0RNL—4119
pp. 8694, .

R. P. Wischner, personal communication to J. R. Engel; March 19, 1971.
 

 

 

X,
X2

Xs

).
X¢
X,

» - Xe
Xo
X10
Xll
Xi2
Xy
X4
Xis
Xue

x1'7

Xie
X9
Xz20

* xa:

=

101

' APPENDIX A

Equations to Describe Xenon and Cover Gas Behavior

Nomenclature

13%mye concentration in pump bowl gas space, atoms/cm

133%e concentration in pump bowl gas space, atoms/cm

195MYe concentration in pump bowl liquid, atoms/cm

135xe conCentration-in pump bowl liquid atoms/tma
135M%e concentration in heat exchanger liquid atoms/cm®
13574 concentration in heat exchanger liquid atoms/cm
135mye concentration in heat exchanger bubbles, atoms/cm

135%e concentration in heat exchanger bubbles,_atoms/cm

_assmgg concentrationgin core liquid atoms/cm

135%e concentration in core liquid, atoms/cm

135Mye concentration in unstripped bubbles in pump bowl, atoms/cm3

13%Xe concentration in unstripped bubbles in pump bowl, atoms/cm®

1331 concentration in fuel salt, atoms/cm

13%%e concentration in graphite pores (central region), atoms/cm
133my, concentration in graphite pores (whole core), atoms/cm
13%Xe concentration in graphite pores (2nd region), atoms/cm®
13570 concentration in graphite pores (3rd region), atoms/cm
ls"‘Xe concentration in graphite pores (outer region), atoms/cm®

"’mXe concentration in piping liquid atoms/cm

13%%e concentration in piping liquid, atoms/cm

135m¥e concentration in piping bubbles, atoms/cm®
 

102
X2z = **°Xe concentration in piping bubbles, atoms/cm*®

X2s = '°°®Xe concentration in core bubbles, atoms/cm®

X2+ = '®*Xe concentration in core bubbles, atoms/cm®

t = time, min.
A = area, ft*
A = radioactive decay!cohstant; min—?

€ = bubble Stripping efficiency
v = region volume,‘ft3

- ¥ = void fraction

F = -flow rafe, saip’or gés, gfim or %/min

H = Hefiry's law ;onstant, moies/éms—atm

R = universal gas constafit, ém’-étm/mole-°K'

T = absolute temperature; °K ”

K = decay fraction

h = mass transfer coefficieni, ft/hr

P | = pressure, psia

P = power, Mw

Y = direct fission yield, fifigfi%fif

o = volume-averaged neufi:on capfiure éoefficient, (Mw-min) ~?
d = bubble diameter, in. o

Dg = diffusion coefficient for xenon in graphite, ft®/hr

r = fadial distance, in.

B = fraction of xenon inventory fransferred from liquid to nucleafied
bubbles ' ' ' -

Z =  cover gas concentration, atoms/cm®

N = number of bubbles, cm—*

'N' = number concentration of bubbles in liquid, cm~3
 

Note:

 

103

Subscripts

Number subscripts, when applied to quantities other than X as
defined above, refer to properties of the region in which the

-variable X with the same subscript may be found. For example,

VFs is the cover-gas void fraction in the region containing X,,
i.e. the core fluid. Double subscripts refer to properties common
to two regions. Thus A,, is the graphite surface area within
region 14 while A;, ;¢ is the graphite interfacial area between
the two regions 14 and 16.

IS_SXe

135mxe

ISSI

- salt-to-graphite

salt-to~graphite in central core region
salt-to-gas bubbies | |

loop -

spray ring

fountain flow

cover gas

ingested purge gaSl

~ reference condition

cover gas
 

 

10.

11.

12.

13.

14.

das _ s _ 2
& V(=T 0 Ty e e MK — g sy

dXs _F,— F, —F; F, +Fy = 7_hb )
at v"z—js 2w, X0 * 7=y Xe * KahiXis A Xs - WT:TJX" W~y b=l
dX, _V¥,9(Fg—~F,—F ' VXT Z
d_t7 = _1—9( {2[5‘«1’5 —f) X1t {‘I’s(F +Fg) — ‘1’19 [F (I —e5)+ F(1—ep)] — } 5 ls =
dXs _ ¥9(F,—F ¥t

Tdt Vg(l—\Ilg)Xs'l'Kmhlxl?' V(l-- )X9 AmXs - %O@-H RTX:3) - V(]

h, A
— A Xjo — D1 0PX0 _J\T(f_Lj(Xlo — HyRTX,4) -

EQUATIONS FOR XENON

 

_ ___InpAs
=t ey K

+ —

 

—F
dt ~ V, \Ifss f) Xaa ¥ {‘I'3(F —Fp) - ‘1’19 [Fs(l —€,) + Fe(1 — )] — } Vo,

dX, . Fy

AIS

MODEL

X,

EL)(X_,, — H,RTX;,)

th]_ 1
H,RTX
fi(& 12)

dX;, _ ¥ h A - F

o Vs & Fre) Xay + 3 O — BRTX) —hy X —g2X, { (B + F) = W15 B2 [Fi(1 ~ €)+ Fe (1 — ¢)] —Fe} v
dX, ¥ h A F
—(fia = V_119 (Fs € + Ff ef) X22 +JV'I_C(X4 - HXRTX2) + hmxl "—?\XXQ —V!'l“ Xz - {\I’:;(Fs + Ff) - ‘I}lg %9- [Fs(l — GS) + Ff(l — Gf)] — Fe}
dX; . F +F; F,+F hy A, | hy A

+ s ~f - — blc - —

a0 V_(_\I!jxlg Km MXyi3 — V3(1 _\pa)X3 AL X3 VL _\ps)(Xg, H,RTX, ) Vil

dX4 F + Ff _ F, +F; _ thc _

dX; _F—-F, —F¢ F, +F; F

| H, RTX,)

| (Xs —H,RTX,)

o(P19/p3) -
VT, st -

Vs¥s

 

 

 

L )(x9 H,RTX 5)

 

 

 

dxlo = Fy Y,P F,

T T =Ty % MK F X + g g - gty X

_ gl — (10 — BRTX, 1) - .7}‘@7()( _ H,RTX,5)
Vg 1 =¥ 10 ™ iy 17 T Vel 10 = 3y
dX,, _ F;+Fg +Ff 6hy,
X3y — Xi1 —ApXi1 +— (X; —HRTX

dt (plQ P3)V3 21 11 11 dR ( 3 X ll)

dX, , F, +Fs F; + F¢ 6hy,
= Xoa t AL X;1 — Xi2 A\ X, +— — H,RTX

dat m 22 P A, X1y v, 12 x12 g (X4 X 12)
dX Y.P
'_d;—s V‘—*szs |
dx14 = CA14 F DGA14 16

-dt

V14f14 16

(X:10 —H RTX14)+—V5h(X“ —X1a) A Xis — A Xjs — P1aPX 4 —F—— Xi4 — Xi6)

 

 

9(P1s/p3) [F (1 —¢) + Fe(1 — )] X2 +\1;’°

X,

Vi

hy As

€s) + Fe(1 — €5)] X4 +V_\F (Xs —H RTX-:)——-X-; - An Xy

As (Xs —HRTXg) +A, X7 — Fy 2 Xs — A, Xs
T, X Vs

 

Bt (Xio —~ HyRTXy) = g2 < (X, — H,RTX, )
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15. d)éés =-11%’E (X, —HXRTXIS)+%8 (Xas = X1s) = A Xis
15 15
16. d’;;" Efififi(xw _H RTx16)+_=gFL1_6(x“ ~X16) F A Xus —AKis — By 6PX1g — pOmlhlS (X, —X;4) - DGR16.17 (X, 4 — Xy1)
1671416 Vielis,i17 _
17, d’;;’ llgéfl(x,o ~H RTX,-,)+-°—EES-.‘-(X24 ~ Xy 1)+ A Xes — A X1 — ®17PXy 5 —3%”;:‘6;:_: X, 1 —xlé)—'\_)fi”:—_’,::: (X;7 — Xys)
18. d’;;“ hSA” (X0 —H RTxls)+_°_&Ffl_l_8(x24 ~Xys) + A Xys — A Xys — ®15PXisg —g%.:_i%(x 18 —X17)
9. d)§;9 =V,9(1FE\I';9)X9 +K M Xis _TF‘I'_IDX” ~AnXie — ““h(bi‘}?—jm” -H RTX“)
19a. d)é;; =V152((11 __\I}fzg)Xg + KnpMXis — -—;-(—lf-g—@-m 9 —ApXi9 —W%(Xlg -—HxR'l;le)
20. d’é:o =V19(1FQ ‘I’lg)Xlo + KA X3 A, Xy — WIPE—TI—;)XZO — A X20 —%(Xzo;—HxRTxn)
20, 0= LT o K Xes A — g oy Koo —MKao — gy (ao — EuRTXzo)
21. d)(i:l =V:I;9£f9 X2 \1,1:):11'99 Xis —HXRTX“)_\%X“ ~AmXa: '
21a. d?:l =V1?£19 X, +$:’?\1;199 (X;9 —H,RTX;,) —»Vifg X1 —Ap X2 }
22, B2 o ol + GBI (Koo — BeRTXas) +AmXat = g Xaz ~AXaz |
22a. % =Vl‘:2§w X1 Vh:’ 22 (Xao — HRTXa2) + A Xay -'% X2z — A Xa2 ;
23. E%-?=%X—, g’%i(xo H RTXza)———Xzs hmxza—vi:{fg X2z — X5) !}
24, d>§:4 \‘,Ifsqu: X, + thg (Xlo H,RTX;4) + A\, X23 _V—x24 ~ A Xz4 — D, 0PX;4 —F_\;;S\%ng_;‘éx24—xl4)—%€£%%—:(x,4 Xi6) ~ &S_FBL(XM...X”) V‘ffi[lj—:’fif(x“_)(”)

 

 
 

109

 

 

 

25.

26.

27.

28.

29.

30.

31.

dz, _
“dt

dZ; _
dt

dZs _

dt

iz,
dt

d¥; _
Tat

a¥s
dt

dvr, _
Tdt

= ~ 22y~ byl
V, =9, "V, & ~gg YT Ty

|
|
{
!

EQUATIONS FOR COVERGAS MODEL

 

 

_F, +F¢ (1 _%3 qr,) Z, - (Fs + Fp)[1 — (p2/p3 )2 ] Z, - h_%AC (Z, - H,RTZ,)
3 2

 

 

_Fa-F-FZy o (Bt FO¥aZy Foy  EfdpV3” o,y prgoygen

 

V3Z4 V3Z4 V3 Z4
_ FeZ, Fo (6/dp)h,¥3/® 2/3
Voo ¥~ ¥s + o Rg 2t (Zs — HRTZ)¥]
z 6/dg )hy ¥
“Ble g By, (/—R)b—z(z., — H_RTZg)¥3/3
V.Zs v,

V2 V2
Fo — Fs — Fq\[1 — (p7/p3)¥+] (Fs + Fp)[1 — (p2/pa )¥2] Zz Fo 6 1;3 (Zs —H,RTZ,;) ;2,3
( Vs ) T-v) 7 v; M=) V2~ & e —g=wy
Fe(1-%5), Fo, 6. i3 —HRIZ) 13 -
=_2 Zy———Zs ——h ¥ Ve i
Vs 1 —T5) ™ Vg™ g 072 (1-¥s) %
;l
_F (1 —‘I’s)z Fo 6 13 (Z7 —HRTZg y2/3 ‘

 

 

 
bt areaba i i s s e a2

 

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12,
13.
14,
15.

: 160’

17.

18.

19.
20.
21.
22.
23.

24,

25.
26.

27.%
28,

29,

730,
31-40.

41,
- 42,

430

44,
45,

46,
470'
- 48, -

49.
50,
51,
52,
- 53,
54.

ST OOH PHOEOQOR®OEOG

-

 INTERNAL DISTRIBUTION

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P. Fraas

H, Frye I
K. Furlong
H. Gabbard
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W. Hoffman

111

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63.
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65.

66.

67,
68.
69.
70.
71.
72.
73.
74,
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76.
77.
- 78,

80.
81.

82.
83.
84.

85.

- 86.
87.
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89.
90.
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93.
94.
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112

102. M. R. Sheldon 112, D. B. Trauger
103. M. J. Skinner : 113. J. S. Watson
104. A. N, Smith ' 114, A. M. Weinberg
105. 0. L. Smith 115. J. R. Weir
106. I. Spiewak ' 116. M. E. Whatley
107. R. A. Strehlow 117. J. C. White
108. D. A. Sundberg 118. G. D. Whitman
109. J. R. Tallackson 119. R. P. Wichner
110. E. H. Taylor 120. L. V. Wilson
111. R. E. Thoma 121. Gale Young

122, H. C. Young

123-124, Central Research Library -
125. Y-12 Document Reference Section

126-127. Laboratory Records Department
128, Laboratory Records (RC)

EXTERNAL DISTRIBUTION

129-130. T. W. McIntosh, AEC, Washington D. C. 20545
131. H. M. Roth, AEC-ORO, Oak Ridge, Tenn. 37830
132. Milton Shaw, AEC, Washington D. C. 20545
133. W. L. Smalley, AEC-ORO, Oak Ridge, Tenn. 37830
134-135. Division of Technical Information Extension (DTIE)
136. Laboratory and University Division, ORO
137. R. C. Steffy, Jr., TVA, 303 Power Building, Chattanooga, Tenn.
37401 ‘
138. A. Houtzeel, TNO , 176 Second Ave., Waltham, Mass. 02154
139-141. Director of Division of Reactor Licensing, Washington D. C. 20545
142-143. Director of Division of Reactor Standards, Washington D. C. 20545
144-148. Executive Secretary, Advisory Committee on Reactor Safeguards,
Washington, D. C. 20545 '