ORNL-4069 by Jon Morrow

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CFSTI P4E?C%S

ORNL-4069

Contract No. W-7405-eng-26

Reactor Division

DEVELOPMENT OF A MODEL FOR COMPUTING 135xe MIGRATION IN THE MSRE R. J. Ked1

A. Houtzeel

L E G A L NbTICE

B. Assumes any liabilities wHb respect to the d e of. or for damapes resulthag from the use of MY Inlorrmtlon. 8&w~ralw. method, or PTOEOSS disclosed In tbls report. As used In the shove. “perm mung 011 behaN of the Commlislon” includes m y employee or contractorof the Commishn. gr omploybe of mch contractor. to the edaat that mch employee or contractor of the Commisslon. 0 employee of ntch contractor prepares, disseminates, or provides ICCOU 00, sng InformatlJ puswit to his employment or contrmt wltb the Cornmisalon. or bls employment Mth such mntrpctor.

JUNE 1967

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee . operated by UNION CARBIDE CORPORATION for t h e U.S. ATOMIC EXEEGY COMMISSION

"?L r.""

...

iii C0"TS Page .

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

Abstract Description of the MSRE Krypton-85 Experiment

.*.. I

........................................ .......................................... Description of the Problem .................................. Description of the Experiment ...............................

........................... ................................ General Approach ............................................ PLmrp Bowl Dynamics .......................................... Xenon Stripper Efficiency ...................................

Procedure and Description of Runs Analysis of the "Kr Experiment

................................... Capacity Considerations ..................................... Xenon-135 Poisoning in the MSRE ................................ General Discussion .......................................... Mass Transfer to Graphite

Dissolved Xenon Source Terms and Considerations Dissolved Xenon Sink Terms and Considerations Other Assumptions and Considerations Xenon-135 Generation Rate

..........

............ ..................... ................................ Xenon-135 Decay Rate in Salt ............................. Xenon-135 Burnup Rate in Salt ............................

................................. .......................... Xenon-135 Migration Rate to Circulating Bubbles .......... Xenon-135 Concentration Dissolved in Salt ................ Xenon-135 Poisoning Calculations ............................ Estimated 13'Xe Poisoning in the MSRE Without Circulating Bubbles ..................................... Estimated 135Xe Poisoning in the MSRE With Circulating Bubbles ..................................... Conclusions .................................................... Acknowledgments ................................................ References ..................................................... Xenon-135 Stripping Rate Xenon-135 Migration to Graphite

1 2

7 7 9

12 18

18 25 29 29 40

41 41 42

43 44

44 44

44 45 47

48 49

-W

.. +

. . . .

53 57 59

Appendix B. Appendix C.

................................... Salt-to-Graphite Coupling ......................... Theoretical Mass Transfer Coefficients J...........

Appendix D.

Nomenclature

Appendix A.

MSRE Parameters

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

65 66

1 DEVELOPMENT OF A MODEL FOR COMPUTING 1 3 5 ~ e MIGRATION I N THE MSRFI R. J. Kedl

A. Houtzeel

Abstract The Molten S a l t Reactor Experiment (MSRFI) i s a fluidf'ueled reactor with a p o t e n t i a l as a thermal breeder. Because of t h e importance of neutron economy t o the breeder concept, it i s necessary t o know the dynamics of 135Xe i n the circulatingf u e l system. There are several "sinks" where xenon may be deposited from t h e fuel, notably i n t h e gas space of the pump bowl and i n t h e voids of t h e unclad graphite of the reactor core. Since 135Xe i n the core impairs the neutron econoqy, it i s important t o understand t h e mass t r a n s f e r mechanism involved and t h e parameters that may be varied t o control it.

This report deals primarily w i t h developing a model f o r computing t h e migration of 135Xe i n the MSRE and with experiments conducted t o e s t a b l i s h the model. A preoperational experiment was run i n t h e MSRE with 85Kr tracer, and many of t h e gas-transport constants were inferred from the r e s u l t s . Equival e n t transport constants f o r calculating the 135Xe migraticn gave a poisoning of about 1.4$ without c i r c u l a t i n g bubbles and well below l$ with bubbles. Preliminary measurements made on the c r i t i c a l reactor show xenon poisoning of 0.3 t o 0.4$. Since physic& measurements confirm t h a t there b e bubbles i n the system, t h e conclusion i s drawn t h a t the computation model, the krypton experiment, and reactor operation agree. The g o a l of t h e Molten S a l t Reactor Program i s t o develop an e f f i -

c i e n t power-producing, thermal-breeding reactor.

The Molten S a l t Reactor

Experiment (MSRE) i s one s t e p toward t h a t goal, although it i s not a breeder.

Nuclear poisons, notably' 135Xe, can d e t r a c t s i g n i f i c a n t l y from

the breeding p o t e n t i a l .

It was therefore considered appropriate t o in-

v e s t i g a t e i n some d e t a i l t h e dynamics of noble gases i n t h i s pilot-plantscaled reactor and with t h i s information t o p r e d i c t quantitatively t h e xenon poisoning. The 135Xe poisoning i s a f'unction of t h e steady-state 135Xe concent r a t i o n - & t h e reactor core.

It i s computed by balancing the r a t e s as-

sociated with the various source and sink terms involved.

Since the MSRT3

i s f l u i d fueled, xenon and iodine are generated d i r e c t l y i n the salt, and

t h e source term is e s s e n t i a l l y a constant. more complex.

The sink terms, however, a r e

Xenon may be removed from t h e system via a s t r i p p i n g de-

vice, it can decay or be burned up i n t h e salt, o r it may be absorbed by t h e graphite and ultimately decay o r burn up.

Xenon may a l s o be absorbed

by c i r c u l a t i n g helium bubbles, which complicate t h e model because of t h e i r r e l a t i v e l y unknown dynamics. This report i s concerned p r i n c i p a l l y with developing a model f o r

estimating the 135Xe poisoning in the MSRE.

However, t h e f i r s t p a r t dis-

cusses an experiment, r e f e r r e d t o as the krypton experiment, i n whi6h

some of the more elusive rate constants were evaluated. DESCRIPTION OF THE MSRE ,

i The MSRE i s a circulating-fluid-fueled graphite-moderated singleregion reactor. The f u e l consists of uranium fluoride dissolved i n a

mixture of l i t h i u m , beryllium, and zirconium fluorides.

The normal oper-

a t i n g temperature i s 1200Â°F, and t h e thermal power l e v e l i s 7.5 Mw.

The

reactor system consists of a primary loop containing the core and a secOur concern i s only with t h e primary loop, a schematic diagram of which i s shown i n Fig. 1. Essentially it

ondary loop t o remove the heat.

consists of a pump, heat exchanger, and reactor core.

A detailed de-

s c r i p t i o n of the MSRE i s contained i n Ref. l, and p e r t i n e n t design parameters are l i s t e d i n Appendix A. Figure 2 shows d e t a i l s of the f u e l pump.

a t a 48.5-ft head.

It i s rated f o r 1200 gpm

--&

The volute is completely enclosed i n a v e s s e l re-

f e r r e d t o as t h e pump bowl, which serves primarily as an expansion volume f o r t h e f u e l salt.

The overflow tank serves as an additional expan-

sion volume f o r t h e system and i s fed by an overflow l i n e t h a t penetrates up i n t o the pump bowl.

The normal operating helium pressure i n t h e pumpâ&#x20AC;&#x2122;

bowl is 5 psig, which i s a l s o t h e pump suction pressure. continuous flow of salt and helium through t h e pump bowl.

There i s a The p r i n c i p a l

s a l t flow i s through t h e xenon stripper, which i s a t o r o i d containing numerous s m a l l holes t h a t spray salt through the helium atmosphere.

The ,

salt flow i s controlled with an o r i f i c e and has been calculated t o be

3 ORNL-DWG 674955

MOTOR

TOTAL FLOW 0.9 STD liter/minl

BUER

XENON STRIPPER.

(2)

JU 1

3FF GAS

:-=3.3 STD liter/min -SAMPLER-ENRICHER PENETRATIW

SALT LEVEL-

voLuTE'mr

PUMP B O W L A

OVERFLOW TAN

FREEZE VALVE FOR FILLING AND DRAINING

Fig. 1. Schematic Diagram of MSâ&#x201A;ŹE Primary Loop. about 50 gpm, but it has not been measured d i r e c t l y .

The r e s u l t i n g high-

v e l o c i t y jets impinging on t h e molten s a l t cause a l a r g e amount of splash'ing and turbulence; consequently, bubbles a r e transported i n t o the loop.

It w i l l be shown l a t e r t h a t a very s m a l l quantity of c i r c u l a t i n g bubbles has a very pronounced e f f e c t on xenon dynamics.

In addition t o t h e s t r i p -

per there i s salt flow of about 15 gpm from behind t h e impeller, through a labyrinth d o n g t h e shaft, and i n t o t h e pump bowl.

The p r i n c i p a l helium

flow through the pump bowl i s 2.4 s t d liters/min purge down t h e shaft t o prevent radioactive gases and salt mist from reaching the bearing region

of the pump. c

"here i s an additional helium flow of 0.9 s t d liters/min -

ORNL-LR-DWG-56043-BRl

I I

@ TAGNANT GAS

To Overflow Tank

Fig. 2.

MSFZ Fuel F'ump. V

from two bubblers and one pressure-reference leg, which comprise the bubbler level indicator. Helium for each bubbler goes through a semitoroid located in the pump bowl, as shown in Fig. 2. Helium enters the semitoroid at the end and leaves in the middle; therefore, half the semitoroid is stagnant gas. This stagnant kidney will be referred to in the analysis of the krypton experiment. Figure 3 is an isometric view of the reactor core.

Fuel salt enters the core vessel through a flow distribution volute and proceeds down an

annular region bounded by the v e s s e l w a l l and t h e moderator container. The f u e l then t r a v e l s upward through the graphite moderator region and out t h e top exit pipe.

Figure 4 shows how the moderator bars f i t to-

gether t o form f u e l channels.

The graphite i s unclad and i n intimate

IBUTOR

Fig. 3 .

Reactor Vessel and Access Nozzle.

contact with t h e f u e l salt, and therefore 135Xe may d i f f u s e i n t o i t s porous s t r u c t u r e ; the graphite a c t s as a 135Xe concentrator i n t h e core. The t h e o r e t i c a l void percentage of MSRE graphite (grade CGB) is 17.7ky and s l i g h t l y over half of it i s accessible t o a gas such as xenon.* Other pertinent properties of this graphite a r e l i s t e d i n Appendix A, and more detailed information i s available i n Refs. 3 and 4 .

The r a t e

a t which 135Xe diffuses t o the graphite . i s a f'unction of t h e s a l t - t o graphite mass t r a n s f e r coefficient, which is, i n turn, a f'unction of t h e f u e l - s a l t Reynolds number. The moderator region can be divided i n t o three f l u i d dynamic regions of i n t e r e s t .

F i r s t there i s t h e bulk of t h e graphite ( - 9 5 $ ) , which i s

characterized by s a l t v e l o c i t i e s of about 0.7 f t / s e c and a Reynolds number of about 1000.

One would expect laminar flow; however, t h e entrance 1

ORNL-LR-DWG

56874R

MODERATOR STRINGERS SAMPLE PIECE

Fig. 4 .

Typical Graphite Stringer Arrangement. V

t o these channels i s o r i f i c e d and quite tortuous because of a layer of graphite g r i d bars across the bottom of t h e moderator t h a t are used t o space and support the core blocks.

The e f f e c t i v e m a s s t r a n s f e r coeffi-

c i e n t i s probably somewhere between t h e c o e f f i c i e n t s f o r laminar flow and turbulent flow.

The second f l u i d dynamic region is composed of the

centermost channels i n the core (about 18).

They do not have o r i f i c i n g

g r i d bars below them, so the f u e l v e l o c i t i e s are higher, about 1.8 ft/sec, and give a Reynolds number of about 2500. Accordingly the mass t r a n s f e r c o e f f i c i e n t i s higher than f o r the bulk of the graphite and i s f o r turbulent flow.

This region comprises about 1.5$ of the graphite and i s i n

a zone of high nuclear importance.

The t h i r d f l u i d dynamic region i s

t h e lower l a y e r of graphite g r i d bars mentioned above, which do the o r i ficing.

These g r i d bars a r e subject t o high s a l t v e l o c i t i e s , a maximum

of about 5 ft/sec,

and comprise a f l u i d dynamic entrance region.

I n ad-

dition, t h e j e t s formed by the g r i d bars impinge on the bottom of the core blocks.

The e n t i r e region then i s subject t o much higher m a s s trans-

f e r c o e f f i c i e n t s than the bulk graphite.

This region i s not too well

defined but probably comprises about 3.5$ of t h e t o t a l graphite.

It i s

i n a zone of very low nuclear importance.

KRYPTON-85 EXPERTMENT Description of the Problem Xenon-135 poisoning i n the MSRE: was considered previously,

5-7

but

these calculations were generally of an approximate design nature because of laclt of information on t h e values of the r a t e constants involved.

In order t o calculate the steady-state 135Xe poisoning i n t h e

reactor, it was f i r s t necessary t o compute the 135Xe concentration dissolved i n t h e salt.

This was done by equating t h e various source and

sink r a t e terms involved and solving f o r t h e xenon concentration.

The

most s i g n i f i c m t 13%e source term i s t h a t which comes from t h e decay of 1351;i n addition a small amount i s produced d i r e c t l y from f i s s i o n . The sink terms a r e discussed i n some d e t a i l l a t e r , but we w i l l i n i t i a l l y

8 consider only the following terms and t h e i r associated r a t e constants: 135Xe Sink Term 1. Dissolved 135Xe t h a t may be transferred t o the off-gas system via the xenon s t r i p per * 2. Burnup of dissolved 135Xe as it passes through core 3.

Decay of dissolved 135Xe

4. Migration of dissolved

l3 5Xe t o the graphite; ultimately this 135Xe w i l l e i t h e r decay o r be burned up

Dissolved 135Xe t h a t may be transferred i n t o circula-

Principal Rate Constants Involved Stripping efficiency

Burnup constant Decay constant

Mass t r a n s f e r coefficient, d i f f'usion c o e f f i c i e n t of xenon i n graphite, decay constant, and burnup constant

Mass t r a n s f e r coefficient, decay constant, burnup constant,

ting helium bubbles, if

and bubble stripping effi-

present; this 135xe w i l l ultimately be burned up, decay, o r be stripped i n the pump bowl

ciency i n t h e pump bowl

The stripping efficiency of the pump bowl spray r i n g was measured

a t the University of Tennessee as p a r t of a masters degree This work was done with a CO2-water system maintained bubble f r e e and l a t e r confirmed with and 02-water system, also maintained bubble f r e e . A prototype of the xenon s t r i p p e r was used i n these t e s t s .

It was f e l t

desirable t o check the r e s u l t s with a xenon and salt system, p a r t i c u l a r l y with c i r c u l a t i n g bubbles present. Xenon-135 burnup and decay r a t e s are r e l a t i v e l y well known.

Migra-

t i o n of xenon t o graphite i s controlled.by the mass t r a n s f e r c o e f f i c i e n t and by t h e diffusion c o e f f i c i e n t of xenon i n graphite.

The mass trans-

f e r c o e f f i c i e n t can be estimated from heat-mass t r a n s f e r analogies (see Appendix C ) , but the unknown mode of f l u i d flow (laminar o r turbulent), the unwettability of graphite by molten salt, the question of mass transf e r t o a porous surface r a t h e r than a continuous surface, and some natural resistance toward assuming a high degree of r e l i a b i l i t y f o r t h e heat-

mass t r a n s f e r analogies made t h e estimated c o e f f i c i e n t s seem questionable. The quantitative e f f e c t of c i r c u l a t i n g bubbles was almost completely

unknown, except that their effect would be prominent because of the ex-

tremely low solubility of xenon in salt.

In addition there may be other effects not considered. Generally the state of knowledge of the rate constants was considered somewhat wanting. Each of these rate constants could be investigated individually in the laboratory, but this would be too expensive and time consuming. Rather, after other approaches were considered, it was decided to conduct a single summary experiment on the \

reactor and extract as many of the rate constants as possible, o r at least set limits on them. The experiment was referred to as the kry-pton experiment. Description of the Ekperiment /

Essentially the experiment was divided into two phases and took place during the precritical period of MSm operations. The first phase was an addition phase and consisted of adding 85Kr to one of the pump-bowl level-indicator bubbler lines at a steady rate for a period of time. During this phase the pump bowl reached some equilibrium 85Kr concentration. almost immediately; then the salt dissolved krypton via the xenon-stripper spray ring; and the graphite absorbed krypton from the salt. The second phase began by turning off the krypton flow but maintaining all bubbler and purge helium flows. Then the reverse processes took place. The pump bowl purged clean of kry-pton; the salt was stripped; and finally t h e graphite w a s leached.

During t h e e n t i r e experiment t h e off-gas l i n e

was monitored continuously with a radiation counter. By analyzing the krypton concentration decay rate in' the off-gas during the stripping , phase of the experiment, we evaluated some of the rate constants involved. The experiment had the advantage of evaluating the actual reactor under operating conditions rather than models under simulated conditions. The experiment had the limitation that several parameters had to be evaluated from essentially a single set of data and were therefore subject to a certain amount of personal interpretation. Also, transient experiments are inherently more difficult to analyze than steady-state experiments. Krypton-85 was chosen f o r the experiment primarily f o r ease of continuous monitoring at low concentrations in the off-gas line; also its low cost and availability were considerations.

10 Figure 5 i s a schematic diagram of the krypton experiment f a c i l i t i e s . Basically, it consists of an addition s t a t i o n and a monitoring s t a t i o n . The addition s t a t i o n controls the flow of an 85fi-He mixture i n t o bubbler l i n e 593.

The normal bubbler flow of pure helium (0.37 s t d liters/min)

was maintained t o transport the krypton-helium mixture i n t o the pump bowl. The reactor contains two bubblers.

The second bubbler was used t o per-

form i t s various reactor control functions. The krypton-helium container was made from 12-in. sched.-80 carbon s t e e l pipe and pipe caps and was about 5 f t long. t e s t e d at 520 psig.

It was hydrostatically

On one end was a U-tube and valve arrangement t h a t

was used t o t r a n s f e r 85Kr from i t s shipping container t o the experiment container. The t r a n s f e r was accomplished by f i r s t evacuating t h e experi,ment container and then opening the valve on the shipping container. This resulted i n about 95% t r a n s f e r . The remaining krypton was transferred by using t h e U-tube as a cold t r a p and freezing it with l i q u i d nitrogen.

ORNL-DWG 67-1956

ROCKER DRIVE BUBBLER LINE 593

-MSRE

LIMITING FLOW VALVE

RAOIATION MONITOR

d MONITOR

V ADDITION SYSTEM

VALVING SET UP-FOR ADDITION PHASE OF EXPERIMENT SALT LEVEL MSRE C i T GAS LINE 522 VOLUT

Fig. 5.

Schematic Diagram of Experimental Equipment.

11 This two-step process resulted i n the almost perfect t r a n s f e r of the 120

curies of 85Kr purchased.

The experiment container was then pressurized

t o 180 psig with heliuml

After the f i r s t run it was f u r t h e r pressurized

with helium t o 275 psig.

Dilution was necessary i n order t o have enough

gas t o measure and control adequately.

The o r i g i n a l 120 curies of 85Kr

amounted t o only about two l i t e r s , and mis had t o be added continuously

t o the reactor f o r a period of several days. Based on experience of the personnel i n the Isotopes Division of

ORNL, krypton mixed with helium w i l l tend t o s e t t l e out over a period of time. To counter t h i s e f f e c t the krypton-helium container was equipped

with a hermetically sealed a g i t a t o r .

It consisted of an 8-in. aluminum

b a l l inside t h e tank that r o l l e d back and f o r t h as the tank was rocked.

A large c o i l of 1/4-in.

s t a i n l e s s s t e e l tubing was located between the

krypton-helium container and flow control equipment t o compensate f o r t h e rocking motion.

The l i m i t i n g flow valve was s e t t o l i m i t the flow

from t h e container t o about 20 s t d l i t e r s / h r i n case of a complete rupt u r e downstream.

The remainder of the flow control system consisted of

conventional f i l t e r s ( 5 t o 9 p), pressure gages, and low-capacity valves. The flowmeter was a Hanover matrix type and was calibrated f o r various o u t l e t pressures.

As shown i n Fig. 5, all the reactor off-gas from the pump bowl went through the monitoring s t a t i o n . It could pass through e i t h e r one of two i d e n t i c a l monitors or a bypass l i n e . The monitors were labeled A and B. Monitor B was used f o r a l l runs. Monitor A was intended as a spare but

was never needed. They were designed f o r a range of f i v e decades of act i v i t y . Each consisted of four amperex 90NB GM tubes, which were shielded as follows : GM Tube

NO.

Shielding '

None

100 mg of p l a s t i c per em2

-100 mg/cm2 q l a s t i c window (7.62 i n 5.9 g/cm brass container

5.9 g/cm2 brass container

2.54 cm)

12 The four GM tubes were suspended i n a 2 - l i t e r stainless s t e e l l a b o l'he monitors were c a l i b r a t e d with s m a l l samples of 85Kr.

r a t o r y beaker.

During the f i r s t run of the experiment, it was found t h a t t h e p l a s t i c shielding on GM tube No. 2 absorbed 85Kr and gave a f a l s e count r a t e ; a l s o it affected other tubes i n the array.

To c o r r e c t f o r this, t h e plas-

t i c 'was removed and GM tube No. 2 became i d e n t i c a l with tube No. 1. The

GM output was fed i n t o a decade s c a l e r and a count r a t e meter. The decade s c a l e r was used f o r recording data, and the count r a t e meter was used f o r experiment control assistance.' Much consideration was given t o the s a f e t y aspect of handling 120 curies of 8

. The h a l f - l i f e of 85Kr i s 10.3 y and it gives off 0.695-

and 0.15-Mev beta p a r t i c l e s and a 0.54-Mev gamma ray. u c t i s 85Rb, which i s s t a b l e .

The daughter prod-

The area i n which t h e experiment w a s con-

ducted was equipped with radiation detectors and air monitors. A continuous flow of a i r (17,000 t o 20,000 cf'm) was maintained through t h e reactor building and released t o the atmosphere through a 100-ft stack. Bricks were stacked around the krypton-helium tank, and t h e a c t i v i t y l e v e l outside the bricks was negligAble.

Special beta-sensitive monitor badges

were worn by personnel operating t h e experiment.

Detailed procedures f o r

t r a n s f e r r i n g 5Kr, pressurizing t h e container, and conducting t h e addition and stripping phases of the experiment were w r i t t e n and approved by appropriate personnel. Procedure and Description of Runs The procedure used t o start the addition phase was t o adjust the krypton-helium container regulator so t h a t the pressure gage just upstream of the main flow control valve was about 10 psig, that is, about

5 p s i over t h e pump bowl.pressure.

The flow rate was then controlled

with t h e main flow control valve.

During t h e addition phase t h e system

was checked every 1/2 t o 1 hr, and t h e flow control was adjusted as necessary t o maintain a constant a c t i v i t y i n t h e off-gas l i n e .

The krypton-

helium container was a g i t a t e d f o r about 15 min every 2 t o 4 hr.

For

various runs t h e krypton-helium i n j e c t i o n r a t e ranged from 2 t o 6.3 s t d

liters/*

but was held constant f o r each run.

Zero time i n the procedure was defined as the time when t h e kry-ptonhelium flow was turned o f f .

This was accomplished by closing t h e krypton-

off valve and then t h e regulating valve.

It took a minute or so before

t h e monitor s t a r t e d dropping because all the l i n e s had t o be purged.

t h e start of the s t r i p p i n g phase, a 1-min count was taken every 1 1/2 min. The times gradually increased u n t i l a t the end of the long runs ( 2 and 3 ) a 1/2-hr count was taken every hour.

Note from Figs. 1 and 2 t h a t

there a r e two e s s e n t i a l l y stagnant l i n e s entering the pump bowl, the sampler-enricher l i n e and t h e overflow l i n e . of

"K,

These l i n e s were purged f r e e

before the s t r i p p i n g phase s t a r t e d and a t various times during

t h e s t r i p p i n g operation. Six 85Kr addition and stripping runs were made. the operational parameters i n these runs. r e s u l t s of these runs.

Table 1 summarizes

Figures 6 through 11 show t h e

The count r a t e i n t h e off-gas monitor i s p l o t t e d

against time during the s t r i p p i n g phase and has been corrected f o r dead time of t h e GM tubes.

No correction was necessary f o r the decay of 85Kr

because i t s h a l f - l i f e i s so long compared w i t h the time scale of each

run. As pointed out previously, the data from run 1 are erroneous because of 85Kr absorbed on the p l a s t i c shielding a GM tube 2. This plast i c was removed f o r subsequent runs. Nevertheless, as an added check, the monitors were purged periodically w i t h pure helium, and a background count was measured. I n a l l cases a f t e r run 1 the background count f o r tubes 3 and 4 was l e s s than 15 cpm. Objectives associated with each run were the following:

Run NO.

Obj ect ive

Check adequacy of equipment and procedures

F i r s t of two long-term runs: get a f e e l i n g f o r the r p s s t r a n s f e r c o e f f i c i e n t from salt t o graphite

Second long-term run: obtain good values f o r mass t r a n s f e r c o e f f i c i e n t t o graphite

Determine s t r i p p i n g kfficiency and other shortterm e f f e c t s with salt l e v e l i n pump bowl a t 61$ scale

Same as 4, with pump bowl l e v e l a t 70% scale

Same as 4, with pump bowl l e v e l a t 55% scale

' a

Table 1. Summary Description of Runs of Krypton Experiment

Run

No.

Addition Phase of Experiment Of

Time

Date

Kr-He Pressure In Pressure ~n Mean Count Ratea Total Total Time Salt Leve1 in Pump Bowl Kr-He Con- &-He ConIn Off-Gas Line Kr-He of from tainer at tainer at Flow Injection Rate During Addition Addition Stripping Level Phase Phase Start Of Run End Of Run (std liters/b) Indicator (counts/min) (PSW (psig) (b) (%scale)

2/5/65 180 179 2.03 6 3570 14 2/6/65 275 240 62 3.57 4470 57.5 2/U/65 240 81 3.67 279 149 4429 4 3/1/65 81 75 5.9 5 -0 6.30 7340 1020 3/2/65 5 75 70 6.24 7081 5.5 7.2 6 Q9X) 3/3/65 70 66 6.33 5.3 12.3 7149 a Count rate as measured by monitor B4, corrected for dead time, and averaged over the entire addition phase. b120 curies 85Kr added to krypton-helium container, and container pressurized to 180 psig with helium before run 1. C Krypton-helium container pressurized to 275 psig with helium between runs 1 and 2.

lb '2 3

1420 ll30 16l3 1545

r- t

(4.

71 60 to 70 â&#x201A;Ź0

61 70 55.5

Total He Flow Through Pump -1 (Purge Plus Bubbler Flaws) (std liters/nin) 3.3 3.3 3.3 3.3 3.3 3.3

K .

1*1) e

ORNL-OWG

67-1957

MONITOR

I I

5 0

I 50

100

150

200

250

300

350

400

450

500

550

TIME

AFTER

*5Kr

FLOW

TURNED

Fig. 6. Results of Krypton Experiment mdnitor corrected for dead time.

OFF (mid

Run 1.

Count rate in off-gas

600

650

700

105

io3

24 28 32 36 TIME AFTER *%r FLOW TURNED OFF (hr)

Fig. 7. Results,of Krypton Experiment Run 2.

___.._I. .,. .

...

_. . ....

. . . .... .__.

CRNL-DWG 67-1959

ALL COUNT RATES CORRECTED FOR DEAD TIME

103

100

TIME AFTER WKr FLOW TURNED OFF (hr)

Fig. 8.

Results of Krypton Experiment R u n 3 .

110

120

130

140

150

18 ORNL-DWG 674960

Kr FLOW WAS TURNED OFF

Fig. 9.

120 150 180 210 TIME AFTER 85Kr FLOW TURNED OFF (min)

240

270

300

Results of Krypton Experiment Run 4.

ANALYSIS OF THE 85Kr EXPEFUNENT General Approach Analysis of t h e 85Kr experiment i s concerned with t h e s t r i p p i n g phase of t h e runs.

The p r i n c i p a l s t r i p p i n g processes involved, i n order

of occurrence, are purging t h e pump bowl, s t r i p p i n g t h e salt and asso-

c i a t e d c i r c u l a t i n g bubbles ( i f present), and then leaching t h e graphite. Other leaching processes of no fundamental i n t e r e s t but of importance because they contribute t o the measured f l u x decay curve a r e diffusion out of the stagnant bubbler kidney described e a r l i e r and leaching 85Kr t h a t may have been trapped i n gas pockets located i n the primary loop. Locations .of p o t e n t i a l gas pockets i n the loop are i n the freeze flanges, graphite access port, and t h e spaces formed by the assembly of the core

ORNL-OWG 67-1961

. e

ALL COUNT RATES CORRECTED FOR DEAD TIME ALL COUNT RATES CONVERTED TO MONITOR 83 READINGS STAGNANT OVERFLOW LINE AND SAMPLER LINE WERE PURGED WITH CLEAN He BEFORE =Kr FLOW WAS TURNED OFF

Fig. 10.

Results of Krypton Experiment R u n 5 ,

ALL COUNT RATES CORRECTED FOR DEAD TIME ALL COUNT RATES CONVERTED TO MONITOR 83 READINGS STAGNANT OVERFLOW LINE AND SAMPLER LINE WERE PURGED WITH CLEAN He BEFORE 85Kr FLOW WAS TURNED OFF PUMP BOWL LEVEL 55.5%

0 0 0

-0 0 0

to5

Iu 0

1 8

21 blocks.

There are various b i t s of evidence that pockets actually exist,

although t h e i r location and capacity are not certain. The f u e l salt c i r c u i t time around the loop i s 25 sec, which i s short compared with t h e time scale of the stripping process involved, so the f i e 1 loop can be considered as a well-stirred pot.

A t any s p e c i f i c time

therefore, t h e krypton concentration i s considered t o be constant throughout the loop.

I n t h e simplest case, it can be shown that each t r a n s i e n t

s t r i p p i n g process, when unaffected by any other stripping process, w i l l . obey an exponential decay law; t h a t i s a t time t, -0%

K r fluxt = K r f l u x e 0

I n the a c t u a l case, however, each stripping process w i l l a f f e c t every other stripping process t o a greater o r l e s s e r extent.

Note t h a t pump

bowl purging, s a l t stripping, and graphite leaching are s e r i e s processes; t h a t is, they occur i n the sequence given; while leachings of the several

graphite regions m e p a r a l l e l processes; t h a t is, they occur simultaneously after t h e krypton concentration i n the salt starts t o drop.

Quali-

t a t i v e l y , the measured decay curve would be expected t o be the sum of t h e contributions of each leaching process, as shown i n Fig. 12.

Note t h a t

ORNL-DWG 67-1963

I I

t i

“I’

CUMULATIVE Kr FLUX FROM REACTOR PURGING Kr IN PUMP BOWL

8 ’

4 S I I

Kr LEACHED FROM VARIOUS GRAPHITE REGIONS

TIME

Fig. 12. Qpalitative Breakdown of Cumulative Flux Decay Curve i n t o I t s Components.

t h e count r a t e i n t h e off-gas line i s p l o t t e d on the ordinate and i s a I

u n i t of concentration; however, since the off-gas i s flowing a t a cons t a n t r a t e , it a l s o represents the 85Kr f l u x leaving t h e reactor. ,

Each

of t h e component curves should approach an exponential decay a f t e r the i n i t i a l transient. Now the problem i s t o separate these individual processes from t h e measured f l u x curve, with t h e r e a l i z a t i o n that there may be other leaching processes not accounted f o r .

It should be pointed out again t h a t

the breaking down of a single composite data curve i n t o several iqdividual i processes and the determination of r a t e constants f o r each i s q u i t e complex and necessarily subject t o a c e r t a i n amount of personal interpretation.

Two approaches were used i n analyzing t h e data.

The most success-

ful method consisted of an exponential peeling technique, as shown qualit a t i v e l y i n Fig. 13 f o r run 3 . The assumption i s made t h a t the t a i l of t h e decay curve i s determined completely by leaching the slow (bulk) r a t e constant graphite.

The procedure was then t o determine t h e equation f o r

t h e slowest exponential t h a t fit asymptotically on t h e curve and subtract

it from the data.

The next exponential equation t h a t f i t asymptotically

ORNL-DWG 67-1964

c 111

CUMULATIVE Kr FLUX FROM REACTOR STRIPPING Kr IN SALT

URGING Kr FROM PUMP BOWL

r LEACHED FROM VARIOUS

TIME

Fig. 13. Actual Method Used t o Break- Down Cumulative Fl& i n t o Its Components.

Decay Curve

on the remaining data was then determined and again subtracted. This procedure was repeated to a logical conclusion; that is, until continued subtracting from the data gave negligible values. This procedure for run 3 resulted in five exponentials, which is somewhat, significant because-ofthe five major stripping operations (pump bowl, salt, including bubbles, and three graphite regions). This general approach is in error in that it assumes that each stripping process starts at zero time and proceeds independently at all others. It will be seen, however, that this approach is adequate for both the very slowest rate constant processes (leaching bulk graphite) and the very fastest rate constant processes (purging pump bowl), but it is inadequate for intermediate processes (stripping salt and faster rate constant graphite). Figure 14 shows the results of this exponential peeling process on run 3 . The rate constants are a fâ&#x20AC;&#x2122;unction only of the slopes of the exponentials involved, so absolute calibrations of the monitor and detailed knowledge of the 85Kr concentrations are not necessary. Numerical results of peeling run 3 and their interpretation are given in Table 2. Thisâ&#x20AC;&#x2122;approach to analyzing the data was the principal method used. It is of necessity confined to the fastest and slowest rate processes involved. But when applied to these processes, the results have a high degree of reliability, as will be seen. A second method of analysis of the data was undertaken primarily as

an attempt to determine rate constants for the intermediate processes involved, such as stripping efficiency and mass transfer to the faster rate constant graphite regions. In this approach, unsteady-state differential equations were set up around the pump bowl gas phase, fuel salt, and three graphite regions. The resulting five equations could be solved simultaneously for the rate constants involved. Physically this was done with a computer, and the rate constants were solved for by the method of steepest ascent. The approach was not too successful, probably for the following reasons: . 1. There were actually mord .thanfive 85Kr sources in the system, so the =thematical model. was overly simplified. .Primarilythe effects

of circulating bubbles were not adequately accounted for,

Fig. 14.

70 80 TIME (hr)

100

120

Results of Exponential Peeling of Krypton Experiment Run 3.

I10

130

140

25 Table 2 . '

Half-Life

b-1

Numerical Results of Peeling Run 3 of Krypton Experiment

Count-Rate Intercept a t Zero Time (counts/min)

198

15.5

4.52 1.039

Rate Constant Determined

3,574

Mass t r a n s f e r t o slowe s t r a t e constant (bulls) graphite

Mass transfer coefficient

2,178

Mass transfer t o next f a s t e r r a t e constant graphite

Mass transfer coefficient

2,114

(a)

4,945 520,000

O.ll9

Process

(b)

punp, bowl purging

Purging efficiency

s o b a b l y influenced mainly by mass transfer t o f a s t r a t e constant graphite but may also be biased by other processes; generally has a low degree of confidence. bProbably influenced mainly by stripping of the salt but is also probably biased by other processes; has a low degree of confidence.

The approach required accurate knowledge of the i n i t i a l concen-

t r a t i o n of t h e krypton i n a l l regions involved (boundary values)

This

could not be done f o r the graphite f o r reasons t o be discussed l a t e r i n the section on Capacity Considerati'ons. The r e s u l t s of t h e second method w i l l not be presented here. Pump Bowl Dynamics

Schematically the pump bowl can be represented as follows:

Monitor Vgp = Volume of gas phase

He purge = ft3/hr a t

Qgp

1200째F

and 5 p s i g

Ck = Average s5K,concen@;

t r a t i o n i n gas phase

_.About

Off-gas line

70'F

Xe s t r i p p e r spray r i n g S a l t phase

Qsp = f t 3 s a l t / h r C$ = 85fi concentration

salt $ =

Void f r a c t i o n

S a l t back t o loop

S = S a l t stripping efficiency S' = Bubble s t r i p p i n g e f f i c i e n c y

The dilution of 85Kr in the gas phase of the pump bowl is given byjc

In the first term Ck is the mean 85Kr concentration in the gas phase of the pump bowl and the product ECk is the concentration in the off-gas Q line; therefore,, E can be thought of as a mixing efficiency. The second term represents the rate at which krypton is stripped from the salt, where S is the stripping efficiency. The third term is the rate at which -kryptonis stripped from the circulating bubbles, where $ is the void frwtion and S I is the bubble stripping efficiency. If these three terms are evaluated at the beginning of the stripping phase, the second term is approximately 1/500 of the first term, so it can be neglected. The third term is about 1/20 or less of the first term for expected values of JI and S I . It must be neglected because of inadequate knowledge of and S ' . The error introduced, however, will not be great. . The above equation also neglects the 85Kr contribution by the stagnant kidney in the bubbler line semitoroid, but estimates indicate that this is also an adequate assumption. Neglecting the second and third terms, the equation is

and, solving for Ck at time t, gives g

which, evaluated at concentration half-life conditions, is *See Appendix D for nomenclature.

or, solving f o r E, 0 693V

E =

2. tl / 2 Q g p

Figures 15 and 16 show the i n i t i a l transients f o r runs 1 through 6. Since the bubbler l i n e stagnant kidney and the salt stripping have l i t t l e

ORNL-DWG 67-1966

A RUN I, HALF-LIFE OF CURVE = 6.8 min 0 RUN 2, HALF-LIFE OF CURVE = 6.3 min

2 .-c

5 c c

I-

a a

ki 3

io3 .

20 25 TIME (mid

Fig 15. Expanded Plot of Data f o r the F i r s t H a l f How of Runs 1 2, and 3. A l l count r a t e data taken with monitor I34 and corrected f o r dead time. 4

28 ORNL-DWG 67-1967

1 RUN 4, HALF-LIFE OF CURVE = 7.6 mir D RUN 5, HALF-LIFE OF CURVE = 6.3 min 3 RUN 6, HALF-LIFE OF CURVE = 8.4 min

2 c

io3

20 25 TIME (min)

Fig. 16. Expanded Plot of Data f o r the F i r s t Half Hour of Runs 4 , All count r a t e data taken with monitor B4 and corrected f o r dead time.

S , and 6.

29 I

effect on the initial transients, this section of the curve is determined almost completely by pump bowl dynamics. A tangent line is shown on each curve and its half-life is given. Note that the half-life measured in the monitor at about 70째F is identical to the reactor half-lives where the operating temperature is 1200째F. Runs 1 through 6 gave the results listed in Table 3. The average pump bowl purging efficiency is 69$, and it is not a strong function of pump bowl level. Table 3 . Pump Bowl Purging Efficiencies Obtained in Runs 1 Through 6 of Krypton Experiment

Run No.

1 2 3

4 5 6

Indicated Pump Bowl Level at Start of Stripping ( 4 scale) 71 60 60

61 70 55.5

Volume of Gas Phase in Pump Bowl ( ft31

Half-Life Of

1.75 2.23 2.23 2.19 1.79 2.43

Curve (mid 6.8 6.3 8.3 7.6 6.3 8.4

Pump Bowl

Purging Efficiency

($1 61 84

64 68 67 68

Xenon Stripper Efficiency As pointed out previously, values for the stripping efficiency could not be extracted from the data with any degree of accuracy, even though runs 4, 5, and 6 were performed with this goal in mind.

Very rough cal-

culations do indicate that the stripping efficiencies are more or less consistent with those measured at the University OT Tennessee in a C02water system, but the calculations are so approximate and dependent on hazy assumptions that they w i l l not be presented here. Mass Transfer to Graphite

To review briefly the graphite regions, recall that three regions were identified from fluid dynamic considerations. First there is the

30 bulk graphite region (-95%) t h a t i s characterized by salt v e l o c i t i e s of

about 0.7 f t / s e c and a Reynolds number of about 1000.

The mass t r a n s f e r

c o e f f i c i e n t w i l l be between t h a t f o r laminar and t h a t f o r turbulent flow. Second, there i s the graphite associated with the centermost f u e l channels, which comprises about 1.5% of the graphite.

The f u e l velocity and

t h e mass t r a n s f e r c o e f f i c i e n t i n t h i s region w i l l be higher than i n the bulk graphite region.

Third, there i s a region of s t r u c t u r a l graphite

across the bottom of the core.

It i s d i f f i c u l t t o determine t h e exact

boundary of t h i s region, but it probably consists of approximately 3.5% of the graphite and i s i n a zone of low nuclear importance.

It i s char-

acterized by o r i f i c i n g e f f e c t s , impingement of salt, and f l u i d dynamic entrance regions; therefore it w i l l have t h e highest mass t r a n s f e r coefficients. The f i r s t question t o be resolved concerns salt-to-graphite coupling v i a the mass t r a n s f e r coefficient.

The krypton f l u x from the graphite

can be expressed as K r flux from graphite = h2AG(c:i

- )C:

where C t i i s conventionally defined as the krypton concentration i n the salt and a t the interface, where the i n t e r f a c e i s continuous. I n this case t h e salt-gas i n t e r f a c e i s inside a pore t h a t occupies only a small f r a c t i o n of the t o t a l graphite s b f a c e area.

Therefore we need a r e l a -

tionship between t h i s concentration a t the pore i n t e r f a c e and the more k conventional Csi. This i s discussed i n Appendix B, where it i s shown t h a t the mean concentration of krypton i n a continuous salt f i l m across the graphite surface i s approximately equal t o the krypton concentration i n the salt at the salt-gas i n t e r f a c e inside a graphite pore. The r a t e a t which "Kr

i s leached from t h e graphite i s a flmction

of several parameters; f o r instance, the d i f f u s i v i t y of krypton i n graphi t e , t h e mass t r a n s f e r coefficient, and t h e

%- concentration dissolved

i n t h e bulk salt, which i s i n t u r n a function of the xenon s t r i p p e r e f f i ciency.

The general approach i n t h e graphite analysis will be t o f i r s t

show t h a t t h i s r a t e i s very insensitive t o expected values of t h e d i f fusion c o e f f i c i e n t of krypton i n graphite.

This being true, we cah

1 . -* r

31 determine a relationship between the mass t r a n s f e r coefficient and the s t r i p p i n g efficiency, any combination of which w i l l r e s u l t i n a f l u x curve

as measured.

Then by weighting t h i s relationship with t h e value of s t r i p -

ping efficiency measured a t the University of Tennessee, t h e o r e t i c a l values f o r the mass t r a n s f e r c o e f f i c i e n t (see Appendix C ) , and other considerations, we w i l l obtain a very narrow range of possible values f o r t h e mass t r a n s f e r coefficient.

Generally, t h i s procedure w i l l be f o l -

lowed f o r all t h e graphite regions considered. i

Most of t h e calculations

w i l l be confined t o run 3, which w a s concerned primarily w i t h measuring

graphite r a t e constants.

i f :

Consider t h e 85Kr f l u x from graphite as a f'unction only of i t s in-

D and i t s external resistance hm * Also specify ( 3 ") f o r times equal t o or greater than zero, the kry-pton concentration

t e r n a l resistance that,

dissolved i n t h e f u e l salt i s zero.

Cylindrical geometry i s used; t h a t

is, each core block i s considered t o be a cylinder, the surface area of I

which i s equal t o the f u e l channel area associated w i t h a single core block. /

The volume of a graphite cylinder of this s o r t i s very close t o

the volume of t h e a c t u a l core blocks of the same length. tial equation t h a t describes t h i s case i s

, w i t h boundary conditions

cGk

ci0 a t t

= 0,

The differen-

The solution to this equation'is

ckG

= 2Ci0

J1(Mn)

1 -

- [Mn) 'D3r;d

n=1 ~n J;(M~) + J:(M~)

where the eigenfunction is

and

where y is the eigenvalue. Now, differentiating with respect to r and evaluating at r = r we have b'

and, substituting into the flux equation at the surface of the graphite,

we obtain

Jp-4 Flux:

- @Mn)2D3r:~]

rbe

n=i Ji(Mn) + Jf(Mn)

From this equation it can be seen that the krypton flux from any given graphite region is the sum of a series of exponentials, with the slope of each expofiential being determined by the exponent of e. The problem now is one of relating these exponents to the slopes of the peeled

f l u x curves.

Considering run 3 it i s obvious t h a t the slowest exponent

( t i / 2 = 198 hr) i s r e l a t e d t o the bulk graphite, and it i s expected that the next exponential ( t i 1 2 = 15.5 hr) i s r e l a t e d t o t h e graphite region located a t the center l i n e of the core.

The next exponential

4.52 hr) has a f a i r l y low order of confidence i n equating it t o any s p e c i f i c

graphite region and w i l l not be considered.

(til2 =

It can be shown t h a t f o r

each of t h e two graphite regions considered, only the f i r s t term of the above s e r i e s i s s i g n i f i c a n t .

Therefore the exponent of e can be r e l a t e d

t o the measured h a l f - l i f e , as follows: *

Now, by evalu ,ting t h i s equation i n conjunction w i t h the eigenfunction k equation, we can r e l a t e values of hm and DG. This was done w i t h the f o l lowing parameter values, and the r e s u l t s appear i n Fig. 17: t i l 2 (bulk til2

E =

(center-line graphite)

= 0.0905

15.5 hr (run 3),

0.10,

H = 8.5 X ,

graphite) = 198 hr (run 3 ) ,

= 6.43

ft, moles/cc*atm,

x 10â&#x20AC;&#x2122;~.

The ordinate represents t h e range i n which Dk i s expected t o l i e . Note G .k t h a t f o r bulk graphite t h e value of hm i s almost completely independent

1 I i

of DG; therefore t h e mass t r a n s f e r c o e f f i c i e n t i s controlling the kry-pton

flux from t h i s graphite region.

For t h e center-line graphite region, t h e dependence of f l u x on Di becomes s i g n i f i c a n t only a t low values of Di. k It is d i f f i c u l t t o e x t r a c t hm information from run 2 because the time i n t e r v a l s involved were too short. ping phases were about 60 hr each.

The krypton addition and s t r i p -

During this r e l a t i v e l y short addition

time t h e bulk graphite reached only about 20% of i t s s a t u r a t e d value, i n contrast t o run 3 , where it reached about 70$ of i t s saturated value.

For both runs t h e center-line graphite region ( t i l 2

15.5 hr i n run 3 )

34 ORNL-DWG 67-1968

10-3

I(r5

5 0

0.t

0.2

0.3

0.4

0.5

0.6

0.7

0.8

hk,,,(ft/hr) k and -h,kThat Fits Graphite Leaching Fig. 17. Relationship Between DG Curves Peeled from Run 3 . was almost completely saturated. After stripping for 60 hr in run 2, the slope of the flux curve is not determined by a single graphite region but is still under the influence of two graphite regions, and it cannot be peeled by the same technique as run 3 . Nevertheless, run 2 was looked at, and without presenting any results, it will be stated that it was consistent with run 3 . k is not a strong f'unction of Di, we can determine the Now, since hm relationship between hk and S (stripping efficiency). This will be done m for the bulk graphite region after sufficient time so that other transients are negligible. First, we will make the following rate balance: Kr flux from xenon stripper = Kr flux from graphite

+ dilution rate of Kr in salt, where k Kr flux from xenon stripper = SQspCs

K r f l u x from graphite

k - Cs),

k B k hm AG(Csi

dCt

Dilution r a t e of Kr i n salt

-Vs

-.d t

Then, substituting, dCff

SQ Ck sp s

hkBA (Ck - C s ) m G si

-V

I n order t o s o l v e t h i s equation, krypton concentrations must be converted t o krypton fluxes because t h i s i s the form of the data.

The measured

krypton f l u x i s r e l a t e d t o the stripping r a t e as follows: /

Flux

k SQspCs

and d flux

dCt

- sQsp

; '

Rearranging gives k

Flux sQsp

and dC:

d flux

sQsp

-=-

and now, confining ourselves t o one graphite region

and s p e c i f i c a l l y t h e

bulk graphite from run 3 ( t i 1 2 = 198 hr), it can be shown t h a t

36 and

â&#x20AC;&#x2122;

Substituting i n t o the above equations gives

and

dCkR

Further, s u b s t i t u t i n g these i n t o the o r i g i n a l r a t e balance we g e t

6g3vs fluxo

+ Solving f o r

c:~

-( 0.693/t1/ -

2)t

gives

fluxo â&#x20AC;&#x2DC;si k - + +k~ --

0.693 /ti

2 )t Y

hm A~

and i n i t s d i f f e r e n t i a l form, c

-dcsi =

4 . 6 9 3 fluxo

*A G

k and dC ./at t o t h e measured slope of t h e f l u x curve and s1 the various physical parameters involved. A t t h i s point we w i l l set up

which r e l a t e s ,C:

a r a t e balance on t h e bulk graphite, as follows: Kr f l u x from graphite = d i l u t i o n r a t e of K r i n graphite,

i 1

where K r flux from graphite

k B k hm %(Csi

- Cs)k , dCE

Dilution rate of K r i n graphite = -VG

-=--

where C E i s the mean krypton concentration i n the graphite. u

Now i n the

previous analysis it was shown t h a t f o r the bulk graphite, h r i s inde1-

pendent of D" over the range of i n t e r e s t . One consequence of t h i s reG sult i s t h a t t h e krypton concentration p r o f i l e acros's a graphite core block i s e s s e n t i a l l y f l a t .

We can therefore s a y t h a t

and also, from Henry's l a w ,

Substituting this into the,graphite rate balance, we have

k dCsi/dt,

Substituting previously derived r e l a t i o n s f o r Csi, t h e above equation, and solving f o r hm, we have,

0.693~

( 1

kB - AGHRTt~/2 m' - 1 j0.693 i

! E

-'G -

SQspti/2

:;;:2J -

(& %) +

and C z i n t o

38 We now evaluate :h

as a f'unction of S f o r the following values of other

parameters :

E =

0.10,

VG = 64.8 f t 3 (volume of graphite i n bulk region),

Vs = 70.5 f t 3 (volume of salt i n loop),

I I1

198 hr (bulk graphite),

A = 1450 f t 2 (channel surface area i n bulk graphite region),

%,2

&SP H

= 50 gpm, =

HRT =

8.5 x 10'' moles/cc*atm, 6.43 x 10'~.

The r e s u l t s of t h i s calculation a r e shown i n Fig. 18, where the mass transf e r coefficient

(e)

i s p l o t t e d against stripping efficiency (S).

Also

this figure the superscript B r e f e r s t o the bulk graphite region.

shown on this p l o t i s the t h e o r e t i c a l expected range of hf-based

ORNL-DWG 67-t969

0.4

a 0.2 W LL v)

a a

Iv) v)

0.1

rE r

0 0

S, STRIPPING EFFICIENCY (%)

100

k Fig. 18. Relationship Between h, and S f o r Bulk and Center-Line Graphite Regions.

39 laminas and turbulent flow; it displays t h e uncertainty i n the d i f f u s i v i t y of krypton i n salt.

I n addition the expected range of stripping e f f i -

ciency i s outlined.

Note that the calculated curves f a l l within the ex-

pected range.

la I n order t o pick out more e x p l i c i t values of hm we can weight this curve with the following two considerations.

F i r s t , it i s expected that

some c i r c u l a t i n g bubbles were present, as w i l l be shown i n the next sect i o n on Capacity Considerations.

Furthermore, it i s expected t h a t c i r -

culating bubbles increase the e f f e c t i v e stripping efficiency t o t h e high end of t h e indicated range, and l i k e l y even highe$.

Second, most of the

s a l t i n t h e bulk graphite region i s of a laminar character, r a t h e r than turbulent, so : h i

ought t o be on the lower end of t h e expected range.

Therefore, from Fig. 18 and w i t h t h e above weighting considerations, we might pick out a probable range of h p t o bulk graphite as 0.05

< hm < 0.09 m

The next graphite region ( t i / Z

ft/hr

15.5 hr), interpreted as the center-

l i n e graphite region, i s more d i f f i c u l t t o handle.

The previous deriva-

t i o n assumes t h a t all the krypton dissolved i n salt comes from the graphi t e region under consideration.

Now, when working w i t h the‘ center-line

region, we must a l s o consider t h e krypton dissolved i n salt t h a t o r i g i nates i n t h e bulk graphite.

An equation whose derivation i s similar t o t h e above and which p a r t i a l l y compensates f o r this i s .”

1 ‘

kCL

where t h e superscripts CL and B indicate center-line and bulk graphite regions, respectively. The equation was evaluated with the same paramee

t e r values as before and with t h e following additional ones, and f o r a given value of S the value of hf

was taken from t h e previous calculation

40 f o r t h e same void fraction: \

CL tl,2 = 15.5 hr (center-line graphite region), ACL = 14.5 f t 2 (chaniiel surface area i n center-line region),

VcGL

Flux:

= 0.682 f t 3 (volume of graphite i n center-line region), = 3574 couiits/min (intercept of peeled curve

at t

= 0 for

0 for

bulk graphite), = 2178 counts/min (intercept' of peeled curve

bulk graphite).

The r e s u l t s of this calculation appear on Fig. 18.

Also shown i s t h e

t h e o r e t i c a l range of h r L based on turbulent flow and displaying t h e unc e r t a i n t y i n d i f f u s i v i t y of krypton i n salt.

The equation f o r h F L i s

invalid a t low values of S because k111y approaches i n f i n i t y ; hence t h e ' l i n e s are terminated as they approach t h e equivalent l i n e f o r h r .

Nev-

ertheless, it 'seems t h a t a reasonable range of hkcL f o r the MSFtE would

be between 0.25 and 0.4 ft/hr. Capacity Considerations

I n addition t o r a t e constant determinations from slopes of t h e peeled exponentials, we should be able t o i n t e g r a t e under the curves and determine information on t h e capacity of t h e system.

For instance, t h e i n t e -

g r a l of the bulk graphite curve (t1,2= 198 hr) should y i e l d the approximate "Kr

capacity of t h i s graphite.

men, from knowledge of t h e "K,

addition concentration, we could compute the approximate graphite void f r a c t i o n available t o krypton.

When this calculation was performed with

t h e addition concentration taken as t h e mean pump bowl concentration, the graphite void f r a c t i o n came out t o be about 0.40.

This i s obviously

incorrect, even when the rough nature of t h e calculation i s considered. The reason f o r t h i s i s t h a t krypton was added through a bubbler, and it bubbled up through the s a l t a t approximately one order of magnitude higher i n concentration than i n t h e pump bowl proper.

These highly concentrated

krypton bubbles were caught i n t h e turbulent and r e c i r c u l a t i n g zone formed by the spray ring.

Very l i k e l y some of these bubbles, o r micro bubbles,

were c a r r i e d i n t o t h e primary loop and c i r c u l a t e d with t h e salt.

The re-

sult was t h a t t h e concentration of dissolved krypton i n t h e f u e l salt was v

41 much higher than it would have been based on the mean pump bowl concentration. Now, if we compute the graphite void fraction based on the dissolved krypton in the salt being in equilibrium with the bubbler addition stream, the result is about 0.04, and this is lower than would be expected. The true void fraction is between the limits of what can be calculated, and insufficient information is available to compute it more accurately. The same is true for all other graphite regions and the fuel salt, therefore little usef'ul information on capacity is available from the data. It should be pointed out that the choice of a bubbler line for 85Kr addition as opposed to the pressure reference leg, which would not have given this deleterious effect, was kictated by other considerations.

XENON-135 POISONING I N "I3 MSFE

General Discussion

To calculate the steady-state 135Xe poisoning in the MSFE, it is first necessary to compute the steady-state 135Xe concentration dissolved in the salt. This is because.the 13*Xe is generated exclusively in the salt, at least it is assumed to be. The xenon concentration in the salt is computed by equating the source and sink rate terms involved. The most significant of these terms and considerations involving them are discussed below. Dissolved Xenon Source Terms and Considerations 1. Xenon Direct f r o m Fission. The 135Xe generation rate direct

from fission 'is about 0.3% per fission. , 2. Xenon from Iodine Decay.. The generation rate is 6.1% per fission, either direct or from the decay of 135Te. It in turn decays to 135Xe with a 6.68-hr half-life. The total 135Xe generation rate is therefore 6.1 + 0.3 = 6.4% per fission, and, as will be seen from the next consideration, is confined completely to the salt phase. Since the principal 135Xe source is from the decay of iodine and since the 1351half-

l i f e i s long compared with t h e fuel-loop cycle time (25 sec), it w i l l be assumed t h a t 135Xe i s generated homogeneously throughout t h e f u e l loop. 3.

Iodine and Tellurium Behavior.

Since

and 135Te a r e pre-

In t h i s model it i s assumed t h a t both elements remain i n solution as ions, and therefore w i l l

cursors of 135Xe, t h e i r chemistry i s important.

not be removed from solution by t h e xenon s t r i p p e r o r diffusion i n t o the Concerning iodine, i t s thermodynamic properties indicate this

graphite.

Recent evidence from the reactor a l s o indicates t h i s t o

t o be true."

Some iodine has been found i n t h e off-gas system (but very lit-

be true.

t l e , i f any,

13%),but

s o r tellurium.

t h i s i s due t o the v o l a t i l i z a t i o n of t h e precur-

Since 135Te has such a s h o r t h a l f - l i f e (63.5 min), very

l i t t l e of it w i l l have a chance t o v o l a t i l i z e ; therefore t h i s e f f e c t i s neglected.

It i s a l s o assumed f o r t h i s model t h a t iodine and tellurium

w i l l not be absorbed on any i n t e r n a l reactor surfaces, such as t h e containment metal and graphite. Dissolved Xenon Sink Terms and Considerations 1. Xenon Decay.

Xenon-135 decays w i t h a h a l f - l i f - of 9.15 hr, and

decay takes place throughout t h e e n t i r e f u e l loop. 2.

of 1.18 3.

Xenon Burnq. X

Xenon-135 has a neutron absorption cross section

lo6 barns averaged over t h e MSRE neutron spectrum. 11

Xenon Stripper Efficiency.

As noted e a r l i e r , t h e efficiency of

the xenon s t r i p p e r was measured a t t h e University of Tennessee with a C02-water system8 and confirmed later with an 02-water system.12 t e s t s were f o r a bubble-free system.

Both

The measured r a t e constants were

The s t r i p p i n g efficiency i s then extrapolated t o a xenon-salt s y ~ t e m . ~ defined as t h e percent of dissolved gas transferred from t h e salt t o t h e gas phase i n passing through the xenon s t r i p p e r spray system.

I n magni-

tude it turns out t o be between 8 and 155. 4 . Xenon Adsorption. Xenon i s not adsorbed on graphite s i g n i f i cantly a t these t e ~ p e r a t u r e s , ~and ~ , ~it~ i s very unlikely t h a t it w i l l be adsorbed on metal surfaces.

Xenon Migration t o Graphite.

The amount of xenon t r a n s f e r r e d

t o t h e graphite i s a function of the mass t r a n s f e r coefficient, diffusion c o e f f i c i e n t of xenon i n graphite, and the burnup and decay r a t e on the

graphite. During manufacture, this graphite was impregnated several times to obtain a low permeability. Diffusion experiments2 with a single sample of CGB graphite yielded a diffusion coefficient of xenon in helium at 1200째F and 20 psig of about 2.4 X cm2/sec (9.2 X ft2/hr). This was measured in a single sample of graphite and may not be representative of the reactor core; however, at w i l l be seen later that the poison fraction in the MSRE is not a strong Fction of the diffusivity.

As previously pointed out, the core graphite may be divided into three fluid dynamic regions, bulk, center line, and lower grid. The krypton experiment did not yield any reliable information on the lower-grid region, and since it is in a region of very low nuclear importance, it will not be considered. The bulk and center-line regions will, however, be considered. 6. Xenon Mimation to Circulating Bubbles. As w i l l be seen, the effect of circulating bubbles is very significant because xenon is so insoluble in salt. Although information on circulating bubbles is meager, they will be considered. Other Assumptions and Considerations 1. The 135Xe concentration dissolved in the fuel salt was assumed

to be constant throughout the fuel loop. From the computed results it can be shown to change less than l$. 2. It was assumed that the 135Xe isotope behaves independently of all other xenon isotopes present.

The 13*Xe generated in the laminar sublayer of salt next to the

graphite was considered as originating in the bulk salt. 4 . The core was considered as being coyosed of 7 2 annular rings, \

as shown below

Core

Core element "e"

Average values of parameters such as neutron flux, percent graphite, mass t r a n s f e r coefficient, etc., were used f o r each ring. 5.

The reactor system was assumed t o the isothermal at 1200oF.

Consistent w i t h all previous assumptions, the r a t e balance of 135Xe dissolved i n the h e 1 s a l t a t steady s t a t e i s the following: Generation r a t e = Decay r a t e i n salt + burnup rate i n salt

+ stripping r a t e + migration rate t o graphite + migration r a t e t o c i r c u l a t i n g bubbles where the u n i t s of each term a r e 135Xe atoms per u n i t time.

Each term

w i l l now be considered separately. . Xenon-135 Generation Rate

The t o t a l 135Xe y i e l d i s 6.44 per f i s s i o n . The corresponding 13%e generation r a t e is 5.44 x 10lg 135Xe atoms per hour a t 7.5 Mw. Xenon-135 Decay Rate i n S a l t The decay of 135Xe dissolved i n salt i s represented as follows: 0. 693VsCz Decay r a t e i n salt

ti/2

Xenon-135 Burnup Rate i n S a l t 1

The burnup r a t e of 135Xe dissolved i n salt i s expressed incrementally by dividing the core i n t o t h e 72 elements described above and is as f o l lows : 72

Burnup r a t e i n salt

e=i

$2emxfeveCz

Xenon-135 Stripping Rate Recalling t h a t the s t r i p p i n g efficiency (S) i s defined as t h e percentage of 135Xe transferred from salt t o helium i n passing through the

45 pump bowl stripper, the stripping rate is expressed as Stripping rate

QSPS C ~

Xenon-135 Migration to Graphite Each graphite core block will be assumed to be cylindrical. This seems to be a good compromise between the trUe case and ease of computation. The surface-to-volumeratio for a cylinder is very close to the channel surface area-to-volume ratio of the actual core blocks. Diffusion of 135Xe inside cylindrical core blocks at steady state and with a sink term is as follows: d2CG dr2

1 dCG

r itr

( 42

x x

A ICG

Solving for the following boundary conditions Cg

= =

finite at r = 0, C& at r = r1â&#x20AC;&#x2122;

we obtain

where

zero-order modified Bessel function of the first kind.

Differentiating and evaluating at rl, we have

The 135Xe flux in the graphite and at the surface (r

rl) is given by

or, substituting the previous equation, we obtain

The 135Xe flux can also be represented by

Flux:

= 1

(c" - S

Combining the last two equations by eliminating CxGi and then solving for Fluxx we obtain

FluZ 1

in units of 135Xe atoms/hr.ft2. Because of the flux distributions, graphite distributions, and the various fluid dynamic regions, the core will be handled incrementally as the 72 regions described earlier. We can now solve for the total 135Xe flux into the graphite, as follows: 72

Migration rate to graphite = e=i

hx meYVeFeCx s h;eHRT 1 + .

Io(Per1) 1&Ber1)

in units of 135Xe atoms per hour, where

Ve F e Y

= = =

volume of core element, graphite volume fraction at Ve, fuel channel surface area-to-graphitevolume ratio.

It is assumed that Y i s constant throughout the core moderator region

and has a value of 22.08 f t â&#x20AC;? . Xenon-135 Migration Rate t o Circulating Bubbles The r a t e of 135Xe migration t o the c i r c u l a t i n g bubbles i s represented

bY Migration r a t e t o bubbles i n u n i t s of 135Xe atoms per hour.

hB$

- Czi)

The salt f i l m i s by f a r the control-

l i n g resistance; therefore the 135Xe concentration i n the bubble i s uniform and a t equilibrium with t h e concentration i n t h e salt a t t h e i n t e r face. Consequently the previous equation can be written as Migration r a t e t o bubbles

6; -)$T,

A t steady s t a t e the migration r a t e t o the bubbles equals the r a t e

t h a t 135Xe i s removed from t h e bubbles, therefore Migration r a t e t o bubbles =Decay rateg + burnup r a t e B + bubble s t r i p p i n g r a t e

where 0 693VsWz

Decryr r a t e i n bubbles

Bubble s t r i p p i n g r a t e

Q $Sâ&#x20AC;&#x2122;C: SP

Burnup r a t e i n bubbles = e=i

4zeoxfeVeWE

and t h e burnup r a t e of 135Xe i n the bubbles i s handled the same as i n t h e

salt, t h a t is, by dividing the core i n t o 72 elements of volume and adding up t h e burnup i n each element. Substituting the individual r a t e terms i n the removal r a t e balance equation we g e t

48 0. 693Vs$€!g

Migration rate to bubbles

72 +

~ 2“feve$cg e

+ Qp’cg

e=i

Now, this equation may be solved simultaneously with the previous equation X to eliminate CB. This results in Migration rate to bubbles

YBc;

hB$HRT

1 +

0.693VsJr X

’

Q2ecxfeVet + Q JrS‘

e=i

in units of 135Xe atoms per hour.

Xenon-135 Concentration Dissolved in Salt The I3*Xe concentration dissolved in salt may now be solved for by substituting the individual rate equations into the original rate balance. This will yield 0.693V Cx 5.44 x

1019

“+E tl/2

42eoXfevecx s

e=i

72 +

x+ QspSCs

hx meYFeVeCx s

e=i

h;eHRT 1 +

1 +

Io(Per11

D D

where the units of each term are 135Xe atok per hour. t

Xenon-135 Poisoning Calculations The xenon poisoning as obtained i n t h i s report i s defined as the number of neutrons absorbed by 135Xe over the number of neutrons ( f a s t and thermal) absorbed by 235U and weighted according t o neutron importance;15 it i s expressed as a percentage. adjoint flux.

When considering t h e core incrementally it i s given by 72

e=1

The weighting function i s the

ax@4 f V C X + 2e 2e e e s

e=i

ax@ 2e $2eFeVeE Gx +

a X 2e @ 42ef eV ew ; e=1

where t h e f i r s t term i n the numerator i s t h e r a t e dissolved 135Xe i s burned up, the second i s t h e r a t e 135Xe i n the graphite i s burned up, and the t h i r d i s the r a t e 135Xe i n the bubbles i s burned up; a l l terms a r e weighted with the adjoint flux.

Now, the term representing the r a t e

135Xe i n t h e graphite i s burned up can be replaced by the 135Xe f l u x i n t o the graphite times t h e f r a c t i o n burned, t h a t i s

With t h i s s u b s t i t u t i o n the poisoning of 135Xe i n the MSRE can be computed. The r e a c t i v i t y c o e f f i c i e n t i s r e l a t e d t o the poisoning by a constant, which i s a function only of t h e nuclear parameters.

This has been evalu-

atedi5 and i s

(Sk/k)x = -0.752 \

Estimated I3%e Poisoning; i n the MSRE Without Circulating Bubbles With t h e equations given above, 135Xe poisoning has been computed f o r t h e MSRE f o r a v a r i e t y of conditions subject t o the assumptions dis-

16, I -

cussed e a r l i e r .

The procedure was t o f i r s t solve f o r t h e steady-state

135Xe concentration dissolved i n t h e salt, and then from this t o compute A code was s e t up t o do these calculations on a computer.

the poisoning.

The neutron fluxes used were those reported i n Eef. 1 5 and corrected with more up t o date information."

Values of many parameters used are given

i n Appendix A, and others were taken from standard reference manuals. Nominal values of various important r a t e constants and other variables were chosen, and the v a r i a t i o n of poison f r a c t i o n with these parameters was computed.

These nominal values may be interpreted as approximate

expected values. situation.

The first case t o be discussed w i l l be the bubble-free

Then the case of c i r c u l a t i n g bubbles w i l l be discussed.

I n the bubble-free case the following nominal values of various parameters were chosen: Available void f r a c t i o n i n graphite, E

Diffusion coefficient of Xe i n graphite, D& f t 3 of void per h r per f t of graphite

0.10 1 x 10-4

Mass t r a n s f e r c o e f f i c i e n t t o bulk graph*, f t / k ite, %

0.0600

Mass t r a n s f e r c o e f f i c i e n t t o center-line graphite, *L, ft/k

0.380

Stripping efficiency of spray ring, S,

12 7.5

Reactor thermal power level, Mw

The pump bowl mixing efficiency was found t o have a negligible e f f e c t and

was not considered. The r e s u l t s of the calculation are given i n Figs. 19 and 20.

Each

p l o t shows t h e poisoning as a function of the parameter indicated, with

all others being held constant a t t h e i r nominal values. dicates t h e nominal value.

The c i r c l e in-

From these p l o t s +he following observations L

can be made.

1. For the bubble-free case, the 135Xe poisoning i n t h e MSRE should be 1.3 t o 1.5%. 2.. Generally speaking the poisoning i s a r a t h e r shallow function of a l l variables plotted.

Note p a r t i c u l a r l y t h e i n s e n s i t i v i t y of poison-

ing t o available graphite void (Fig. x)) and the diffusion c o e f f i c i e n t (Fig. 20) ite.

: The reapon i s t h a t h

controls the 135Xe f l u x t o t h e graph-

This _could be an important economic consideration i n f u t u r e Peactors

51 ORNL-DWG 67-1970

0 MASS TRANSFER COEFFICIENT

- BULK GRAPHITE (ft/hr)

MASS TRANSFER COEFFICIENT

- CENTER-LINE GRAPHITE (ft/hr)

STRIPPING EFFICIENCY ( O h )

Fig. 19. Predicted 135Xe Poison Fraction i n t h e MSRE Without C i r culating Bubbles a t 7.5 Mw(t) . ' See body of ' r e p o r t for values of other parameters.

of this type. For instance, if xenon poisoning is the only consideration, the permeability specifications may be relaxed somewhat. Other numbers of interest are given below. For the nominal case, the 13%e distribution to its sink terms is

2 c

.\"

0 *

0 REACTOR THERMAL POWER LEVEL (MW)

0 DlFFUSfON COEFFICIENT OF Xa IN GRAPHITE (ft2/hr)

Fig. 20. Predicted 135Xe Poison Fraction in the MSFU?, Without Circulating Bubbles at 7.5 Mw(t). See body of report for values of other parameters.

53 Decay i n s a l t Burnup i n salt Stripped from salt Migration t o graphite

3.48 0.9 31.0

64.7 100.0%

O f the 135Xe that migrates t o the graphite, 52$ i s burned up and 48% de-

cays, averaged over the moderator region.

Again, f o r the nominal case,

96.4% of t h e , t o t a l poisoning i s due t o 135Xe i n the graphite and only 3.6% i s due t o the 135Xe dissolved i n the s a l t . Estimated 135Xe Poisoning i n the MSRF: with Circulating Bubbles '

Xenon, and all noble gases f o r t h a t matter, i s extremely insoluble

i n molten salt.

From the Henry's l a w constant, Cf = 2.08 x

Cx a t 1200'F g

where the u n i t s of concentration are xenon atoms per u n i t volume.

A sim-

p l e calculation would show t h a t with a c i r c u l a t i n g void f r a c t i o n of 0.01 and t h e xenon i n the l i q u i d and gas phases i n equilibrium, about 98% of t h e xenon present would be i n t h e bubbles, or i f t h e void f r a c t i o n i s 0.001, 83%of t h e xenon would be i n the bubbles.

We would therefore ex-

pect that a s m a l l amount of c i r c u l a t i n g helium bubbles would have a pronounced e f f e c t on 135Xe poisoning. Circulating bubbles have been observed i n the MSRE. The most sign i f i c a n t indications come from "sudden pressure release t e s t s I f These

experiments c o n s i s t of slowly increasing t h e system pressure from 5 t o

15 psig and then suddenly venting the pressure off.

During t h e pressure

release phase, t h e s a l t l e v e l i n the pump bowl r i s e s and t h e c o n t r o l rods are withdrawn; both'motions indicate t h a t c i r c u l a t i n g bubbles are present. Void f r a c t i o n s can be computed from these t e s t s t h a t range from 0 t o 0.03 but are generally l e s s than 0.01.

The reactor operational parameters

t h a t control t h e void f r a c t i o n are not completely understood, and it appears t o be a q u i t e complex phenomenon.

rnw

For instance, the void f r a c t i o n

be a function of how long the reactor has been operating. The bubble diameter i s extremely d i f f i c u l t t o estimate.

"he only

d i r e c t source of information on t h i s point i s from a water loop used f o r

54 MSRE pump t e s t i n g . I n t h i s loop the pump bowl i s simulated with Plexiglas so t h a t the water flow can be observed. The bubbles t h a t migrated from the pump bowl i n t o the pump suction could be seen and were about the s i z e of a "pinpoint." For lack of any b e t t e r measurement they were taken t o be i n the order of 0.010 in. in diameter. As w i l l be seen, t h i s i s not a c r i t i c a l parameter i n these calculations. Information i n the l i t e r a t u r e on mass t r a n s f e r t o c i r c u l a t i n g bubbles i s meager.

Nevertheless, from Refs. 16 through 19 and other sources,

the mass t r a n s f e r c o e f f i c i e n t was estimated t o be i n t h e range 1 t o 4 ft/hr and p r a c t i c a l l y independent of diameter.

Again it turns out t h a t

t h i s i s not a c r i t i c a l parameter, even over t h i s fourfold range.

It i s

a l s o assumed that t h e existence of c i r c u l a t i n g bubbles w i l l have no eff e c t on the salt-to-graphite mass t r a n s f e r coefficient. This i s equiva-

l e n t t o saying t h a t t h e c i r c u l a t i n g bubbles do not come i n contact with the graphite i n any s i g n i f i c a n t quantities. A parameter that i s quite c r i t i c a l i s t h e bubble s t r i p p i n g e f f i -

ciency.

This i s defined as t h e percentage of 13%e enriched bubbles t h a t

burst i n passing through t h e spraJr r i n g and a r e replaced with pure he-

l i u m bubbles. value i s .

A t t h i s time there i s no good indication as t o what t h i s

It i s probably a complex parameter l i k e the circulating-void

f r a c t i o n and depends on many reactor operational variables. any b e t t e r information, a nominal value was taken as

lo%,

For lack of

because this

i s about the s a l t s t r i p p i n g efficiency, but it could j u s t as e a s i l y be

i n t h e order of 100%. Xenon-135 poisoning has been computed f o r t h e following range of variables pertaining t o c i r c u l a t i n g bubbles. Parameter Mean c i r c u l a t i n g void volume

Nominal Value

Range Considered

Mean bubble diameter, in.

0 010

Mean bubble mass t r a n s f e r coefficient, ft/hr

2.0

Mean bubble s t r i p p i n g e f f i ciency, $

*loo

Again t h e nominal value can be interpreted as the expected value but with

All other parameters

much l e s s c e r t a i n t y than i n the bubble-free case.

not pertaining t o the bubbles were held constant a t t h e nominal value given f o r the bubble-free case.

Figures 21 and 22 show the computed

13*Xe poisoning as a f b c t i o n of c i r c u l a t i n g void volume with other parameters ranging as indicated.

Parameters not l i s t e d on these p l o t s were

ORNL-DWG 67-1972

1.4 1.2

1.0

0.8

0.6

0.2

0.25

0.50

0.75

MEAN BUBBLE CIRCULATING VOID ("/o)

1.00

1.25

6.I-

ORNL-DWG 67-1973

1.4

1.2

--ae

1.0

0.8 0 v)

0.6 a n X

0.4

0.2 0

0.25 0.50 0.75 1.00 MEAN BUBBLE CIRCILATING VOID (70)

1.25

1.0 5

-ae z 8g -

2 0.1

2 0.01 5 fb/

0.1

0.2

0.3 0.4 0.5 0.6 0.7 0.8 MEAN BUBBLE CIRCULATING VOID (%I

0.9

t.0

1.1

Fig. 22. Predicted 135Xe Poison Fraction in the MSRE with CircuSee body of report for values of other lating Bubbles at 7.5 Mw(t). parameters held constant at their nomind values. From these figures, the following observations can be made:

1. Circulating bubbles have a very pronounced effect on 135Xe poisdning, even at very low void percentages. 2. The 135Xe poisoning is a rather weak function of the bubble mass transfer coefficient and diameter over the expected range. 3 . The poisoning is a strong function of the bubble stripping efficiency..

57 Figure 22 also shows the contribution of each system (salt, graphite, and bubbles) to the total 135Xe poisoning. All parameters are fixed at their nominal values. This figure illustrates how bubbles work to lower the poisoning. As the circulating void is increased, more and more of the dissolved xenon migrates to the bubbles, as noted by the rapidly increasing contribution to poisoning by the bubbles. In contrast to the bubble-free case in which the 135Xe in the graphite is the greatest contribution to poisoning, the 135Xe concentration of the salt is rapidly reduced by the bubbles and is thus not available to the graphite. At the time this report was written, there was no accurate knowledge of the extent of 135Xe poisoning. Preliminary values based on reactivity balances indicate it is.in the range 0.3 to 0.4.k. This is considerably below the value calculated for the bubble-free case, but it is well within the expected range when circulating helium bubbles are considered. We conclude therefore that this model probably does accurately portray the physical reactor, and good agreement depends only on reliable values of the various parameters involved. Work is currently under way to estimate more accurately the circulating void fraction and to determine what operational variables affect it. An attempt will also be made to estimate the bubble stripping efficiency, although this may be quite an elusive parameter to evaluate. Actually, the most recent information seems to indicate that the circulating void fraction ($) is in the order of 0.1 to 0.3% and the bubble stripping efficiency ( S I ) is in the range of 50 to 1008. Equipment is currently being built to measure 135Xe poison fractions more accurately.

CONCLUSIONS The a n a l y s e s presented indicate the following: 1. A transient experiment such as the 85Kr experiment can be useful . in determining rate constants and other information for a complex process . are serious limitations, such-as noble gas dynamics in the MSRE. There however, and a detailed study should be made beforehand.

58 2. The krypton experiment indicated t h a t mass t r a n s f e r c o e f f i c i e n t s computed from heat-mass t r a n s f e r analogies a r e q u i t e good f o r t h e moltens a l t porous-graphite system. 3 . If t h e MSRE could be operated bubble free, t h e computed 135Xe However, the reactor does not

poisoning would be 1.3 t o 1.5s a t 7.5 Mw.

operate bubble free, so t h e poisoning should be considerably l e s s . This r e s u l t s from the extreme i n s o l u b i l i t y of xenon i n salt. When t h e model i s modified t o include c i r c u l a t i n g bubbles, t h e computed values can be made t o agree with preliminary measured values (0.34.4s) by adjusting bubble parameters used over reasonably expected ranges. ~

It would seem

therefore t h a t the model does portray the p m s i c d reactor.

However,

t o prove t h i s conclusively, we must have accurate knowledge of the bubb l e parameters, and with these calculate precisely the 135Xe poisoning. We think the model i s q u i t e representative of this system and can e a s i l y be extended t o other fluid-fueled reactors of this type.

This model should not.be taken as f i n a l .

assumed t h a t iodine does not v o l a t i l i z e .

For instance, it was

If it i s l a t e r determined t h a t

iodine does v o l a t i l i z e , t h e model w i l l have t o be-adjusted accordingly.

5. The c i r c u l a t i n g helium bubble concept should be considered ser i o u s l y as a 135Xe removal mechanism i n future molten-sa2t reactors. Helium bubbles could be injected i n t o t h e flowing salt a t the core o u t l e t and be removed with an i n - l i n e gas separator some distance downstream. 6.

The i n s e n s i t i v i t y of 13%e poisoning t o t h e graphite void frac-

t i o n and diffusion c o e f f i c i e n t should be noted.

This indicates t h a t the

t i g h t specifications of these variables f o r t h e s o l e purpose of lowering t h e 135Xe poisoning might not be necessary.

Considerable savings could

be r e a l i z e d i n f u t u r e reactors.

This phenomenon occurred i n the MSRF: be-

cause the f i l m c o e f f i c i e n t i s t h e controlling mechanism f o r t r a n s f e r of 135Xe t o t h e graphite.

Each future reactor concept would have t o be

studied i n d e t a i l t o assure t h a t t h i s was s t i l l t r u e before t h e above statement was applicable.

ACKNOWLEDGMENTS

We are indebted to H. R. Brashear of the Instrumentation and Controls Division for designing, building, and calibrating the radiation detectors used to monitor l8*Kr,, to T. W. Kerlin of the Reactor Division for his assistance in the unsteady-state parameter evaluation used in the krypton experiment analysis, and to the members of the MSRE operating staff for assistance in preforming the krypton experiment.

REFERENCES 1. R. C. Robertson, MSRE Design and Operation Report, Part I, Description of Reactor System, USAEC Report ORNL-TM-728, Oak Ridge National Laboratory, January 1965

2. Oak Ridge National Laboratory, Reactor Chemistry Div. Ann. Progr. Rept. Jan. 31, 1965, USAM: Report ORNL-3789. 3. Oak Ridge National Laboratory, Molten-Salt Reactor Program Semiann. Progr. Rept. July 31, 1966, USAEC Report ORNL-3708. 4. F. F. Blankenship and A. Taboada, M3RE Design and Operation Report, Part IV, Chemistry and Materials, USAM: Report ORNETM-731, Oak Ridge National Laboratory (to be published) 5 . I. Spiewak, Xenon Transport in MSRE Graphite, Oak Ridge National Laboratory, unpublished internal report MSR-60-28, Nov. 2, 1960. 6. G. M. Watson and R. B. Evans, 111, Xenbn Diffusion in Graphite: Effects of Xenon Absorption in Molten Salt Reactors Containing Graphite, O a k Ridge National Laboratory, unpublished internal document, Feb. 15, 1961. 7. H. S o Weber, Xenon Migration to the MSRE Graphite, Oak Ridge National Laboratory, unpublished internal document. 8. J. R. Waggoner and F. N. Peebles, Stripping Rates of Carbon Dioxide from Water in Spray m e Liquid-Gas Contactors, University of Tennessee Report EM 65-3-1, March 1965. 9. ktter from F. N. Peebles to Dunlap Scott, March 31, 1965, Subject: Converting Stripping Rates from CO2-Water System to Xe-Salt System. 10. F. F. Blankenship, B. J. Sturm, and R. F. Newton, Predictions Concerning Volatilization of Free Iodine from the MSRE, Oak Ridge National Laboratory, unpublished internal report MSR-60-4, Sept. 29, 1960 11. B. E. Prince, Oak Ridge National Laboratory, personal comunication to authors. 12. F. N. Peebles, University of Tennessee, personal communication to authors '\ 13. FLJ. Salzano and A. M. Eshaya, Sorption of Xenon in High Density Graphite at High Temperatures, Nucl. Sci Eng., 12: 1-3 (1962). 14. M. C. Cannon et al., Adsorption of Xenon and Argon on Graphite, Nucl. Sci. Ehg., 12: 4 4 (1962). 15. P. N. Haubenreich et al., MSRE Design and Operation Report, Part 111, Nuclear Analysis, USAEC Report ORNL-TM-730, Oak Ridge National Laboratory, Feb. 3, 1964. 16 E. Ruckenstein, On Mass Transfer in the Continuous Phase from Spherical Bubbles or Drops, Chem. Ehg. Sci., 19: 131-146 (1964).

17.

Id e t al., Unsteady S t a t e Mass Transfer For G a s Bubbles

18.

P. Harriott, Mass Transfer t o Particles, Part I

Suspended i n A g i t a t e d Tanks; Part I1 Suspended i n a Pipeline, Amer. I n s t . Chem. I Engrs. J., 8(1) : 9 3 1 0 2 (March 1962).

19.

S. Sideman e t

Liquid Phase Controlling, h e r . I n s t . Chem. Ehgrs. J., ll(4): 581-587 (July 1965)

al., Mass Transfer i n Gas-Liquid Contacting Systems, 58(7): 3 2 4 7 (July 1966).

20.

R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 1 9 a . I

21.

C. V. Chester, Oak Ridge National Laboratory, personal comrrmnication t o authors.

j 1

APPENDICES /

65 '

Appendix A

Msm

PARAMETERS

General Normal thermal power level, Mw Nominal operating temperature, OF Operating pressure in pump bowl, psig Fuel salt flow rate, gpm Fuel salt volume, ft3 Graphite volume, fi3 Xenon stripper flow rate (estimated), gpm Salt flow along Shaft to pump bowl, Total bypass flow (sum of above), gpm Fuel loop circuit time, sec Graphite Grade BUUC density, g/cm3 Porosity, accessible to kerosene, $ Porosity, theoretical, $ Porosity, available to xenon and krypton," $ Fuel salt absorption at 150 psig (confined to surface), $ Wettability Graphite surface area in fuel channels, f t 2 Diffusivity of Kr at 1200'F in graphite (filled with He), ~r atoms/hr.ft graphite (aatoms/ft3 gas) Diffusivity of Xe at 1200'F.in graphite (filled with He), Xe atoms/hrafi graphite (xe at0ms/ft3 gas) Equivalent diameter of fuel channels in bulk graphite, ft Fuel Salt Liquidus temperature, OF Density at 1200'F, lb/ft3 Viscosity at 1200'F, lb/ft*hr Dif'fusivity of Kr at 1200'F (based on several estimated values), ~'/hr Diffusivity of Xe at 1200'F (based on several estimated values), f t 2 / h r Henry's law constant for Kr at lXH)"F, moles of Kr per cc of salt per atmosphere Henry's law constant for Xe at 1200'F, moles of Xe per cc of salt per atmosphere

*From Ref.

2. 'Not wet by fie1 s a l t at operating conditions.

7.5 1200 5 1200 70.5 69

50 15 65 25.2 CGB 1.82-1.87 4.0 17.7 -10 0.M

t 1520 -1.0 x 10-4 4.92 x iom4 0.0519

840 130 18 4.3 x 10-~~.0 x 10'~ 3.9 x m54.4 x 10-~ 8x x 2.75 x 10'~

Appendix B SALT-TO-GRAPHITE COUPIJNG

A question e x i s t s concerning the process of mass t r a n s f e r from a

f l u i d t o a porous medium as opposed t o a continuous o r homogeneous medium.

For example, the krypton f l u x from graphite t o salt i s given by Fluxk = h 3 G

(c:f - Cff) ,

1 where A i s the t o t a l channel surface area of t h e graphite. !the term G k hm i s defined so t h a t C s f i s not the kry-pton concentration i n s a l t a t

the salt-gas phase i n t e r f a c e (located a t a pore opening), but r a t h e r i s some continuous concentration across the e n t i r e surface of t h e graphite. This i s shown schematically below and would be similar f o r t h e case of

xenon flowing from s a l t t o graphite.

Direction of Kr Flow

boundary Layer

- V//////

bning He and K r

>m Region of Conventional Mass T----*-Where l$, Is Applicable

The mean pore entrance diameter f o r CGB graphite i s l e s s than 0.1 c1 and probably closer t o 0.02 boundary layer thickness.

which i s extremely small compared with the

It seems,reasonable, therefore, t h a t krypton

i s transported from t h e pore opening t o the continuous concen$ration l a y e r Then from the continuous l a y e r t o t h e

by a process of pure diffusion.

bulk salt, krypton w i l l be transported by conventional f l u i d dynamic mass

transfer.

Note that since s a l t w i l l not wet graphite, and because of

the s m a l l pore size, the salt-gas i n t e r f a c e w i l l c e r t a i n l y not penetrate inside a pore.

Also inherent i n t h i s analysis i s the idea that salt w i l l

touch t h e s o l i d graphite matrix, even though i t . w i l l not wet it, and therefore t h e salt-gas phase i n t e r f a c e w i l l e x i s t only a t the pore opening.

In order t o couple the s a l t t o the graphite, it i s necessary t o k

develop a relationship between Csf k t h a t Csi

and Csi.

Actually it w i l l be shown

k Csf.

I n this development we consider a simplification of the previous figure, as follows :

Boundary Layer

Pore

The pure diffusion region hssociated with a single graphite pore i s approximated i n spherical geometry.

' W

The inner hemisphere a t constant con-

and radius ri i s the source f o r krypton t h a t diffuses k through salt t o t h e outer hemisphere a t constant concentration Csf and

centration iC:

radius rf' Associated with each pore is a unit transfer cell of crosssectional area m;, through which krypton is transferred by conventional mass transfer,fromthe position of to the bulk salt at concentration is taken as half the mean pore entrance diameter 'and rf Ci. The term r. 1 is related to it with the graphite void fraction.

!@e general equation for diff'usion in spherical coordinates at steady state, and when concentration is a function only of the radius, is d2C: 2 dC: -+---0 dr2 rdr Solving with boundary values, as discussed above, T.

1 - -'i r .ri 1 - 7 f

k- k s' 'si k k 'sf - 'si

Differentiating with respect to r, dC: --

k ri Csf --

k - Csi

'f Substituting into the flux equation, define'd as follows, dC:

Fluxr

= -$A

gives k

F~ux = 'DsAr ~

i' 'sf r2 1 :

- 'si ri

/ '

Then, solving at r

rf for a hemisphere (Ar

2rrr:), we obtain

k k Ck sf - â&#x20AC;&#x2DC;si Fluxr = -2rrriDs ri f . 1--_ â&#x20AC;&#x2DC;f

Without going into the considerations, we will state that a reasonable relationship between ri and rf is ri

( 7c y 2 .

Substituting this in,o the equation for fluxr gives f

Now, at steady state, this diffusion flux at rf must equal the convective flwc.throughthe unit cell, where

Therefore, equating flux and fluxunit cell, we obtain rf SI

Solving for the following parameter values,

$ = 4.26 I

e ri

x 10-5 ft*/hr, 0.06 ft/hr (approximate for bulk graphite region),

0.1 P (actually probably closer to 0.02 P),

E =

rf '

0.10,

= 0.446 P,

we obtain

1 .

k Csf k 'si

- cs k - 'sf

217

k and Ctf is negwhich says that the concentration difference between Csi ligible compared with the difference between Ctf and Ct. Another way of

putting it is that Cii M Cif. pendix can now be written

The equation at the beginning of this ap-

Fluxk = h : A G ( c i

-):C .

71 Appendix C THEOHTICAL MASS TRANSFER COEFFICIENTS

Theoretical mass t r a n s f e r coefficients between f u e l s a l t and graphi t e may be estimated by using standard heat t r a n s f e r coefficient relationships and the analogy between heat and mass transfer.

These conversions

a r e brought about by substitution of equivalent groups from the following t a b l e i n t o the appropriate heat t r a n s f e r coefficient relationship.

They

apply f o r e i t h e r laminar o r turbulent flow. Heat Transfer Quantity

PdeqV -

NY-n = Pr=

Mass Transfer Quantity

2 k

hmdeq n u

IJ sc,= PD

Applying these substitutions t o the Dittus-Boelter equation f o r turbulent flow, we have, 1.

f o r heat transfer, k

(+) pd

O**

r4)Oo4,

1i !

l i

f o r mass transfer,

For laminar flow the following equations can be used: 1. f o r heat transfer,

72 \ 2. for mass transfer,

D 1.86 d &e eq

113

1.86

Calculated values of hm for krypton would then be as follows:

%, Mass Transfer Coefficient (ft/hr) Bulk Graphite

Turbulent flow

O.ll50.155

L u n a r flow

0.048-0.067

Center-Line Graphite Region 0.250-0.338

k where the range in hm reflects the range of Ds given in Appendix A. This range in DkS represents an expected range as determined from three sources: 1. as measured indirectly21 from analogy of the noble gas-salt system to the heavy-metal ion-water system, , 2. estimated from the Stokes-Einstein equation,

estimated from the Wilke-Chang equation.

73 Appendix D NOMENCIATURE

Surface area

Noble Noble Noble Noble

cg CG CS

Units

Definition

Term

gas gas gas gas

concentration concentration in gas phase concentration in graphite concentration in salt

ft2 atoms/ft3 atoms/n3 atoms/ft3

Heat capacity Equivalent diameter of flow channel Diffusivity

atoms/ft3 Btu/lb OF ft ft2/hr

Pump bowl purging efficiency

Void fraction of graphite Volume fraction of salt in element Ve

CP deq

Volume fraction of graphite in element Ve

Neutron flux Henry's law constant for salt Heat transfer coefficient

neutrons/cm2-sec moles/cc atm Btu/hr-ft2*"F

Mass transfer coefficient

ft/hr

Modified Bessel functions of the first kind Bessel functions of the first kind Thermal conductivity Length of fuel channel Radioactive decay constant Poisoning

Btu/hr-ft*OF

H %l

J k

L h

ft hr-1

Volumetric flow rate Volumetric flow rate of helium at 1200째F and 5 psig through pump bowl

ft3/hr ft3/hr

Volumetric flow rate of salt through xenon stripper

ft3/hr

Radius Radius at equivalent core block in cylindrical geometry

(43

(

Units

Definition

Term R

Universal gas constant

cc .atm/째K*mole

Density of s a l t

lb/ft3

Stripping efficiency, defined as the percentage of dissolved gas transferred from l i q u i d t o gas phase as salt i s sprayed through the xenon s t r i p p e r

Bubble s t r i p p i n g efficiency, defined as the percentage of 135Xe containing bubbles t h a t burst i n passing through the s t r i p p e r and are replaced w i t h pure helium bubbles

Absorption cross section

barns

Time

tl/2 T

. Half-life

Absolute temperature

O K

Fluid v e l o c i t y

ft/sec

Volume of salt i n primary loop

ft3

Volume of graphite i n core

ft3

Volume a t gas phase i n pump bowl

ft3

Volume of core element e

ft3

Arbitrary constant

Viscosity

lb/f t hr

Ratio of f u e l channel surface a r e a t o graphite volume i n core

ft'l

Average void f r a c t i o n of helium bubbles c i r c u l a t i n g with salt i n primary loop

vgP

Superscripts P

l35

8 5~

23 5u

B CL

~ e

Adjoint f l u x Mean

Bulk graphite region Center-line graphite region

hi,

Subscripts

Fast neutrons

Thermal. neutrons

Boundary

Circulating bubbles

Element of core volume

Film Gas phase Graphite Heat

Interface Mass

Initid conditions

Putup bowl

At radius r

Salt phase

-8

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