EARCH LIBRAR DOCUMENT COLLECTION cut I i ORNL-4069 3 445L 0487570 3 UC-80 — Reactor Technology DEVELOPMENT OF A MODEL FOR COMPUTING 135y e MIGRATION IN THE MSRE R. J. Kedl A. Houtzeel OAK RIDGE NATIONAL LABORATORY CENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION LIBRARY LOAN COPY DO NOT TRANSFER TO ANOTHER PERSON 1f you wish someone else to see this document, send in name with document and the library will arrange a loan. OAK RIDGE NATIONAL LABORATORY operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION 4" Ll Contract No. W-7405-eng-26 - : Reactor Division i DEVELOPMENT OF A MODEL FOR COMPUTING 135%e MIGRATION IN THE MSRE R. J. Kedl A. Houtzeel JUNE 1967 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S5. ATOMIC ENERGY COMMISSION ORNL-4069 43 iii ADSETECT teveereessrossnusssssaesarsessssnesssassssssassssnssass Description of the MSRE ...t ivicirivsnnesnsannsnnnns e eseseaann Krypton-85 Experiment ...... [P UL Description of the Problem ...... ettt eetaeeren e Description of the Experiment .....ccceveeeneesosnncrcesnnnes Procedure and Description of RUNS ceveeveaseesococoenes e Analysis of the %°Kr Experiment ..... Ceareasee cenene EERE R General Apprbaéh ........... e e, Pump Bowl DynamicCsS cvveeeessssssosnsceosssosoasnanosassossensns ‘Xenon Stripper Efficiency ...ccciveceeean. e PRSP Mass Transfer to Graphite ......cce..0.., R R P PR Capacity Considerations .........oeuieeuieiieninnerenioeneanen Xenon-135 Poisoning in the MSRE ......ccvvieeincencnnnannennannns General DiSCUSSION v eeeeeesseerossssssssossorasesocsossoasassass ‘ Dissolved Xenon Source Terms and Considerations ...cecse.. Dissolved Xenon Sink Terms and Considerations ............ Other Assumptions and Considerations ..ececeeeeeeeieeeeses Xenon-135 Genération Rate ....... eheeeaas e eeeesseae e Xenon-135 Decay Rate in Salt ...veieereessencsnnnns [ Xenon-135 Burnup Rate in Salt ...cveeiieivinrenieeccnsanens Xenon-135 Stripping Rate .. .iiii it eiin i, Xenon-135 Migration to Graphite .....ovceeivereennvenenns . PR | Xenon-135 Migration Rate to Circulating Bubbles ..... e Xenon-135 Concentration Dissolved in Salt ....covveeniesss . | Xenon-135_Poisoning Calculations ..ccecevcorvensencenseronsons Estimated 13°Xe Poisoning in the MSRE Without Circulating Bubbles ..uveereeeeencersessvacersronronnocnos Estimated 1°°Xe Poisoning in the MSRE With Circulating BubbleS teeeeeeeereeneanrencessssssassnnnonns CONCLUSIONS setevasesvoaseossosoosssssasasesoossssonasssaasssansass Acknowledgments ........................................ e References .v.oveeciesssssaasrssassssses e e s s e acseas e s e resses s s an s s ena Page 12 18 18 25 29 29 40 41 41 41 42 43 42, 44, 44, 44, 45 4 48 49 49 53 57 59 60 Appéndix A. Appendix B. Appehdix C. Appendix D. iv MSRE ParametersS .eveeeeecscescearescasonsotcaacosses Salt-to-Graphite Coupling ............ P | Theoretical Mass Transfer Coefficlents «.ieeveen ;.. Nomenclature 65 66 71 73 o A » > DEVELOPMENT OF A MODEL FOR COMPUTING 135Xe ‘ MIGRATION IN THE MSRE - R. J. Kedl A. Houtzeel ~ Abstract The Molten Salt Reactor Experiment (MSRE) is a fluid- ‘fueled reactor with a potential as a thermal breeder. - Because of the importance of neutron economy to the breeder concept, it is necessary to know the dynamlcs of 135Xe in the circulating- fuel system. 'There are several "sinks" where xenon may be de- posited from the fuel, notably in the gas space of the pump bowl and in the voids of the unclad graphite of the reactor core. Since *25Xe in the core impairs the neutron economy, it is important to understand the mass transfer mechanism involved and the parameters that may be varied to control it. ‘This report deals prlmarlly with developing a model for computing the migration of '2°Xe in the MSRE and with experi- ments conducted to establish the model. A preoperational ex- periment ‘was run in the MSRE with 85Ky tracer, and many of the gas-transport constants were inferred from the results. Equiva- lent transport constants for calculating the 135%e migraticn -gave a poisoning of about 1. 4% without circulating bubbles and . well below 1% with bubbles. Preliminary measurements made on the critical reactor show xenon poisoning of 0.3 to O. 4% Since physical measurements confirm that there are bubbles in the sys- .. tem, the conclusion is drawn that the .computation model, the. - krypton experiment, and reactor operation agree. The goal of the Molten Salt Reactorwfrogram is to develop an effi- 01ent power- producing, thermal- breedlng reactor.‘ The Molten Salt Reactor Experlment (MSRE) is one step toward that goal although it is not a hreeder. Nuclear poisons, notably_1?5Xe, can detract 51gn1f1cantly from the breedlng potentlal It was therefore considered appropriate to in-. vestlgate in some detall the dynamlcs of" noble gases 1n thls pllot—plant— scaled reactor and with this information to predlct quantltatlvely the xenon p01son1ng.l llhe 135Xe p01son1ng is a function of the steady-state 135Xe concen- tratlon in the reactor core. It is computed by balan01ng the rates as- soc1ated with the varlous source and sink terms 1nvolved. Since the MSRE is fluid fueled xenon and iodine are generated directly in the salt and the source term is essentially a constant. The sink terms, however, are more complex. Xenon may be removed from the system via a stripping de- vice, it can decay or be burned up in the salt, or it may be absorbed by; the graphite and ultimately decay or burn up. Xenon may also be absorbed by circulating helium bubbles, which complicate the model because of their reiatively unknown dynamics. 7 This report is concerned principally with developing a model for estimating the 135%e poisoning in the MSRE. waevef, the first part dis- cusses an experiment, referred to as the krypton experiment, in which some of the more elusive rate constants were evaluated.- ‘DESCRIPTION OF THE MSRE The MSRE is a circulating-fluid-fueled graphite-moderated single- region reactor. The fuel consists of uranium‘fluoride dissolved in a mixture of lithium, beryllium, and zirconium fluorides. The normal oper- " ating temperature is 1200°F, and the thermal power level is 7.5 Mw. The reactor system consists of a primary loop containing the core and a sec- ondary loop to remove the heat. Our cohcern is only with the primary loop,>a schematic diagram. of which is shown.ianig. 1. Essentially it consists of a pump, heat -exchanger, and reactor core. A detailed de- scription of the MSRE is contained in Ref. 1, and pertinent design pa- rameters are listed in Appendix A. | | Figure 2 shows detalls 6f the fuel pump. If is rated for 1200 gpm at a 48.5-ft head. fhe volute is cdmpletely enclosed in a vessel re- ferred to as the pump bowl, which serves primarily as an expansion vol- ume for the fuel salt. The overflow tank serves as an additional exXpan- sion volume for the system and is fed by an overflow line that penétfates up into the pump bowl. The normal operating helium pressure in the pump bowl 1s 5 psig, which is also the pump suction pressure. There is a continuous. flow of salt and helium through the pump bowl. The pfincipal' salt flow is through the xenon stripper, which is a toroid containing —— numerous small holes that spray salt through the helium atmosphere. The salt flow is controlled with an orifice and has been calculated to be o) -P(‘l 3 v ORNL-DWG 67-1955 T TOTAL FLOW - { BUBBLER .PRESSURE Ref. FURGE GAS w24 'STD liter/min ) i in] - : ' A 09 STO liter/min BUBBLER (2) O o8 33 STD liter/min . . ——— YXENON STRIPPER SAMPLER-ENRICHER PENETRATION - SALT LEVEL PUMP BOWL VOLUTE SECONDARY 'SYSTEM PIPING OVERFLOW TANK| ‘ . CONTROL ROD CONNECTIONS 2, .. . SALT FLOW RATE, N 00 gpm « = I // ’{/ ercese rance UhFREEZE FLANGE CORE RN FREEZE VALVE FOR JFILLING AND DRAINING Fig. 1. Schematic Diagram of MSRE Primary Loop. about 50 gpm, but it has not been measured directly. The resulting high- 1 velocity jets impinging on the molten salt cause a large amount of splash- \1ng "and turbulence, consequently, bubbles are transported into the loop. N ‘It will be shown later that a very small quantity of” c1rculat1ng bubbles has a very pronounced effect on xenon dynamlcs. Tn addition to the strip- per.there’is salt flow of about 15 gpm from behind the impeller, through a lahyrinth aleng the shaft, and into the pump bowl. The principal.helium flow through the pump bowl is 2.4 std‘liters/min purge down the shaft to ‘ prevent ‘radioactive’ gases ‘and salt mist from reachlng the bearlng region of the pump . There is an additional helium flow of 0.9 std llters/mln . , ~ B 4 - R ORNL-LR-DWG-56043-BR! . | ] T C — 3 — SHAFT ' gi:; —3 .. SWATER COUPLING . 0 ) A, o, COOLED . A MOTOR SHAFT SEAL e — D ) NS S e e vty § R R LEAK = _ 1 DETECTOR— : : LUBE OIL BREATHER LUBE OIL IN } } ‘ - BALL BEARINGS: ; S e F R (Face to Face) BEARING HOUSING =~ BALL BEARINGS ! GAS PURGE IN - $ (Back to Back ) SHAFT SEAL LUBE OIL OUT _ SHIELD COOLANT PASSAGES SEAL OIL LEAKAGE ' S | | (In Parallel With Lube 0Qil) DRAIN SHIELD PLUG s By : : I 4 'LEAK DETECTOR GAS PURGE - OUT SAMPLER ENRICHER GAS FILLED EXPANSION ) (Out of Section) ] ‘ i SPACE g | , XENON STRIPPER HELIUM BUBBLER ‘ (Spray Ring) = = d— SPRAY OPERATING v | T M7 =1 [ LEVEL o - el _//// > S E HELIUM BUBBLER ' ' PUMP BOWL CONFIGURATION \ I To Overflow Tank ) Fig. 2. MSRE Fuel Pump. from two bybblers and one pressure-referenée leg, which comprise the bub- ‘bler level indicator. Helium for each bubbler goes through a semitoroid " located in the pump bowl, as shown in Fig. 2. Helium enters the semi- toroid at the end and leaves in the middle;. therefore, half the semi- toroid is stagnant gas. This stagnant kidney will be referréd_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 % 3 annular region bounded.by the vessel wall and the moderator container. The fuel then travels upward through the graphite moderator region and F out the top exit pipe. The graphite is unclad and in intimate igure 4 shows how the moderator bars fit to-- gether to form fuel channels. ORNL-LR- DWG 61097RS n T (] T o o 3 n 7] Fw w o ) -2 z z =1 - = oo - @ o Zz - o OCo < o O J® - o W z o) o - a O . o b O wn wZ O - N Lw _.n.w_ w Q -4 REACTOR ACCESS PORT 1< o - > @ 1 - a o = o - TR — QUTLET STRAINER MODERATOR AR 2 J \) {0 \\;W\v,”“;.rlfl.fl.rl%pa@géfififigw e . B . L ACRA, o) | s . B\ fl\'tv L. . YA e B i ST e g | o fl@ it wll)) BN s O | = \,...!.‘nn.\ ! Gm 5 =) " & i &\m *h A b -y GRAPHITE SAMPLE ACCESS PORT FUEL OQUTLET CONTROL ROD THIMBLES / i 4 { o & fo i : | i ¢ o ; VESSEL DRAIN LINE CORE CENTERING GRID FUELINLETJ/fi GRAPHITE-MODERATOR\ _ STRINGER ! REACTOR CORE CAN—" REACTOR VESSEL— ANTI-SWIRL VANES SUPPORT GRID Reactor Vessel and Access Nozzle. Fig. 3. (3 contact with the fuel salt, and therefore ;35Xe may diffuse into its porous structure; the graphite acts as a *?°Xe concentrator in the core. The theoretical void percentage of MSRE graphitel(grade CGB) is 17.7%, and slightly over half of it is accessible to. a gas such as xenon. © Other pertinent properties of this graphite are listed in-Appendix A, and more detailed information is available in Refs. 3 and 4. The rate at which 12%Xe diffuses to the graphite is a function of the salt-to- graphite mass transfer coefficient, which is, in turn, a function of the fuel-salt Reyndlds number. v The moderator region can be divided into three fluid dynamic regions " of interest. First there is the bulk of the graphite (~95%), which is characterized by salt velocities of about 0.7 ft/sec and a Reynolds num- ® ber of about 1000. One would expect laminar flow; however, the entrance ORNL-LR-DWG 56874 R PLAN VIEW TYPICAL MODERATOR STRINGERS SAMPLE PIECE Fig. 4. Typical Graphite Stringer Arrangement. .‘v ' to these channels is orificed and quite tortuous because of a layer of graphite grid bars across the bottom of the moderator that are used to space and support the core blocks. The effective mass £fahsfer coeffi- cient is probably somewhere between the coefficients for laminar flow and turbulent flow. The second fluid dymamic regién.is éompdsed of the centermost channels in the core.(about 18). They do not have orificing grid bars below them, so the fuel velocities are higher, about 1.8 ft/sec, and give a Reynolds number of about 2500. Accordingly the mass transfer coefficient is higher than for the bulk of the graphite and is for tur- bulent flow. This region comprises about 1.5% of the graphite and is in a zone of high nuclear importance. The third fluid dynamic'region is the lowerhlayer of graphité'grid bars mentioned above, which do the ori- ficing. These grid bars are subject to high salt velocities, a maximum of about 5 ft/sec, and comprise a fluid dynamic entrance region. In ad- difiion, the jéfs'forméd-by tfie grid bars impinge on the bottom of the core blocks. The éntire région then is.- subject to much higher mass trans- fer coefficients than the bulk graphite. This region is not.too well defined but probably comprises about 3 5% of the total graphlte It is 1n a zone of very low nuclear 1mportance. KRYPTON~85 EXPERIMENT - Description of the Problem _ Xenon-135 poisoning in the MSRE was considered prev1ously,5 7 but these calculatlons were generally of an approximate design nature be- cause of lack of 1nformatlon on the values of the rate constants 1n- volved. In order to calculate the steady-state 135Xe poisoning in the reactor, it was first necessary to compute. the }?5Xe_concentrat10n dis- éolvéd in the salt. This was done by equating the various source and sink rate terms involved and- solving for the .xenon concentration.. The most significant_135Xe source term is that_whiqh comes from the decay of .72°I; in addition a small amount is produced directly from fission. The sink terms are discussed in some detail later, but we will initially consider only the following terms and their associated rate constants: Principal Rate 135 : . Xe Sink Term Constants Involved 1. Dissolved '?°Xe that may be Stripping efficiency transferred to the off-gas ' ' system via the xenon strip- per 2. Burnup of dissolved 135%e as Burnup constant it passes through core ‘ 3. Decay of dissolved '3°Xe ' Decay constant Migration of dissolved 135%e Mass transfer coefficient, dif- to the graphite; ultimately fusion coefficient of xenon this 13°Xe will either de- in graphite, decay constant, cay or be burned up and burnup constant 5. Dissolved *3°Xe that may be = Mass transfer coefficient, de- transferred into circula- cay constant, burnup constant, ting helium bubbles, if and bubble stripping effi- present; this 135%e will ul- ciency in the pump bowl timately be burned up, de- cay, or be stripped in the pump bowl Thé stripping efficiency of the pump bowl spray ring was méasured at the University of Tennessee as part of a-masters degree thesis.®»? This work was done with a CO,-water system maintained bubble free and later confirmed with and O,-water system, also maintained bubble free. A prototype of the xenon stripper was used in these tests. It was felt desirable to check the results with a xenon and salt system, particularly with circulating bubbles present. | Xenon-135 burnup and decay rates are relatively well known. Migra- tion of xenon to graphite is controlled by the mags transfer coefficient and by the diffusion coeffiéient of xenon in graphite; The mass trans- fer coefficient can be estimated from heat-mass transfer analogies (see Appendix C), but the unknown mode of fluid flow (laminar or turbulent), the unwettability of graphite by moltep salt, the question of mass trans- fer to a porous surface rather than a continucus surface, and some natu- ral resistance toward assuming a high degree of reliability for the heat- mass transfer analogies made the estimated coefficients seem questionable. The quantitative effect of circulating bubbles was almost completely L)) > " 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 wénting. Fach 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, or at least set limits on them. The experiment was referred to as the krypton experiment. Description of the Experiment Essentially the experiment was divided into two phases and took place during the precritical period of MSRE 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. Dur- ing this phase-the pump bowl reached some equilibrium 85Ky concentration almost immediately; then the salt dissolved krypton via the xenon-strip- per 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 krypton;'fhe salt was stripped; and finally the graphite was leached. During the entire experiment the off-gas line 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 éome of the rate constants in- volved. The experiment had the advantage of evaluating the actual reac- tor under operating conditiohs rather than models under simulated con- ditions. The experiment had.thg limitation that several parameters had to be e#aluated 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 for the experiment primarily for ease of continuous monitoring‘ét low concentrations in the off-gas line; also its low cost and availability were considerations. 10 ~ Figure 5 is a schematic diagram of the krypton experiment facilities. Basfically, it consists of an addition station and a monitoring station. The additiofi station controls the flow of an ®°Kr-He mixture into bubbler line 593. The normal bubbler flow of fiure helium (0.37 std liters/min) was maintained to transport the krypton-helium mixture into the pump bowl. The reactor contains two bubblers. The second bubbler was used to per- form its various reactor control functions. | The krypton-helium container was made from 12-in. sched.-80 carbon steel pipe and pipe caps and was about 5 ft long. It was hydrostatically tes%ed at 520 psig. On one end was a U-tube and valve afrangement that Was!used‘to transfer 85Kr from its shipping container to the experiment container. The transfer was accomplished by first evacuating the experi- | | N ment container and then opening the valve on the shipping container. This resulted in about 95% transfer. The remaining krypton was transferred by using the U-tube as a cold trap and freezing it with liquid nitrogen. ORNL-DWG 67-1956 ROCKER DRIVE |, —MSRE BUBBLER . ¥ LIMITING FLOW VALVE ' ' R:\%gll\l?TTéJ%N ¥ ' e I PRESSURE REGULATOR A o E A|_|:‘| - Kr-He \. /' CONTAINER FREEZE , -4 5 o i - X e MONITOR SYSTEM CONTROL VALVE ADDITION SYSTEM VALVING SET UP FOR ADDITION PHASE OF EXPERIMENT |m. . f I, MSRE OFF GAS LINE 522 Fig. 5. Schematic Diagram of Experimental Equipment. (2. 11 This two-step process resulted in the almost perfect transfer of the 120 curies of %%Kr purchased. The experiment container was then pressurized to 180 psig with helium. After the first run it was further pressurized ‘with helium to 275 psig. Dilution was necessary in order to have enough gas to measure and control adequately. The-original. 120 curies of 85Ky amounted to only about two“liters, and this had to be added continuously to:the.reactor for a period of several days. | Based on expefience of the personnel in the Isotopes Division of ORNL, krypton mixed with helium will tend to settle out over a period of time. To counter this effect the krypton-helium contéiner was equipped with a hermetically sealed agitator. It consisted of an 8-in. aluminum ‘ball inside the tank that rolled back and forth as the tank was rocked. A large coil of 1/4-in. stainless steel tubing was located between the krypton-helium container and flow control equipment to compensate for the rocking motion. The limiting flow valve was set to limit the flow from the container to about 20 std liters/hr'in case of a complete rup- ture downstream. - The remainder of the flow control system consisted of conventional filters‘(5 to 9 u), pressure gages, and low-capacity valves. The flowmeter was a Hanover matrix type and was calibrated for various outlet pressures. As shown in Fig. 5, all the reactor off-gas from the pump bowl went through the monitoring station. It could pass through either one of two identical monitors or a bypass line. The monitors were labeled A and B. Monitor B was used for all runs. Monitor A was intended as a spare but was never needed. Théy were designed for a range of five decades of ac- tivity. ZEach consisted of four amperex 90NB GM tubes, which were shielded as follows: . GM Tube No. Shielding - 1 - None 100 mg of plastic per cm? ~100 mg/cm? plastlc window (7.62 X 2. 54 cm) in 5.9 g/cm brass container 4 5.9 g/cm brass container 12 The four GM tubes were suspended in a 2-liter stainless steel labo- ratory beaker. The monitors were calibrated with small samples of 8 5kr. During the first run.of the experiment, it was found that the plastic shielding on GM tube No. 2 absorbed 85kr and gave a false count rate; also it affected other tubes in the array. . To correct for this, the plas- tic waé removed and GM tube No. 2 became identical with tube No. 1. The GM output was fed into a decade scaler and a count rate meter; The de- cade scaler was used for recording data, and the count rate meter was | used for éxperiment control assistance. Much consideration was given to the safety aspect of handling 120 curies of 85Kr. The half-life of 8%Kr is 10.3 y and it gives off 0.695- and 0.15-Mev beta particles and a 0.54-Mev gamma ray. The daughter prod- l L) uct is 85Rb, which is stable. The area in which the experiment was con- ducted was equipped with radiation detectors énd air monitors. A con- tinuous flow of air (17,000 to 20,000 cfm) was maintained through the re- actor building and released to the atmosphere through a 100-ft stack. Bricks were stacked around the krypton-helium tank, and the activity level outside the bficks was negligible. Special beta-sensitive monitor badges were worn by personnel operating the experiment. Detailed procedures for transferring 8?Kr, pressurizing the container, and conduéting the addition and stripping phases of the experiment were written and approved by ap- propriate personnel. Procedure and Description of Runs The procedure used to start the addition phase was to adjust the krypton-helium container regulator so that the pressure gage just up- O - stream of the main flow control valve was about 10 psig, that is, about 5 psi over the pump bowl pressure. The flow rate was then controlled , . with the main flow control valve. During the addition phase the system was checked every 1/2 to 1 hr, and the flow control was adjusted as nec- essary to maintain a constant activity in the off-gas line. The krypton- helium container was agitated for about 15 min every 2 to 4 hr. .For various runs. the krypton-helium injection rate ranged from 2 to 6.3 std liters/hr but was held constant for each run. ) 13 'Zero time in the procedure was defined as the time when the krypton- helium flow was turned off. This was accomplished by closing the krypton- off valve and then the regulafing valve. It‘took a minute or so before the monitor started droppihg because all the lines had to be purged. At the start of the stripping phase, a l-min count was taken every 1 1/2 min. The times gradually increased until at the end of the long runs (2 and 3) a l/2—hr count was taken every hour. Note from Figs. 1 and 2 that there are two essentially stagnant lines entering'the pump bowl, the sam- pler-enricher line and the overflow line. These lines were purged free of 87Kr before the stripping phase started and at various times during the stripping operation. | Six 8%Kr addition and stripping runs were made. Table 1 summarizes the operational parameters in these runs. Figures 6 through 11 show the results of these runs. The count rate in the off-gas.monitor is plotted against time during the stripping phase and has been corrected for dead time of the GM tubes. Nb correction was necessary for the decay of 8 5Ky because its half-life is so long compared with the time scale of eéfih run. As pointed out previously, the data from run 1 are erroneous be- cause of 8°Kr absorbed.on the plastic shielding a GM tube 2. This plas- tic was removed for subsequent runs. Nevertheless, as an added check, the monitors were purged periodically with pure helium, and a background count was measured. In all cases after run 1 the background count for tubes 3 and 4 was less than 15 cpm. Objectives associated with each run were the following: Run No. ' Objective 1 Check adequacy of equipment and procedures First of two long-term runs : get a feeling for the mass transfer coefficient from salt to graphite 3 Second long-term run: obtain good values for mass transfer coefficient to graphite 4 " Determine stripping efficiency and other short- term effects with salt level in pump bowl at 61% scale Same as 4, with pump bowl level at 70% scale 6 Same as 4, with pump bowl level at 55% scale Téble 1. Summery Description of Runs of Krypton. Experiment Starting Time Pressure In Pressure In Mean Count Ratea Total Total Time Salt Ievel in Total He Flow CKrypton—helium container pressurized to 275 psig with helium between runs 1 and 2. L2 of Addition oy con- Kr-He Con- Kr-He In Off-Gas Line Kr-He of Pump Bowl Through Pump Run Phase of . . Injection - s ‘s - from Bubbler : ) tainer at tainer at During Addition Addition Stripping : Bowl (Purge Plus No. Experiment Flow Rate Level Start of Run End of Run . Phase (hr) Phase - Bubbler Flows) ; : (std liters/hr) . Indicator td 1iters/mi Time Date (951g) (psig) (counts/min) (hr) (% scale) (std liters/min) 1P 1420 2/5/65 180 179 2.03 3570 6 14 71 3.3 2% 1130 2/6/65 275 240 3.57 4470 57.5 62 60 to 70 3.3 3 1613 2/11/e65 240 81 3.67 4429 279 149 &0 3.3 4 1545 3/1/65 81 75 6.30 7340 5.9 5.0 61 3.3 5 1020 3/2/65 75, 70 6.2 7081 5.5 7e2 70 3.3 6 0920 3/3/65 70 66 6.33 7149 5.3 12.3 55.5 3.3 ®Count rate as measured by monitor B4, corrected for dead time, and averaged over the en- tire addition phase. 'bl20 curies 8%Kr added to krypton-helium container, and container pressurized to 180 psig . with helium before run 1. 71 (.) COUNT RATE (counts/min) n * ORNL-DWG 67-1957 1) \ MONITOR B2 ] 10 \ 1 \ 5 \MONITOR B3 | N\ 2 4 —— \MONITOR B4 4 L ] 10 A ‘ - \ . || 5 - O . 50 100 150 200 250 300 350 400 450 500 550 . 800 650 700 TIME AFTER ®°Kr FLOW TURNED OFF (min) Fig. 6. Results of Krypton Experiment Run 1. Count rate in off-gas monitor corrected for dead time. T ORNL-DWG 67-1958 16 105 (Uwysgunod) 31y INNOD TIME AFTER ¥ FLOW TURNED OFF (hr) T T T I, uw O¢ H04 440 dWNd T3N3 . O . (o) N © . 10 . ' u P . —HES N b ok . u3 . 0,.= " : 1 o) M m = . o ] e ] 0w . ¥ = . [ & . 2y : & Z H 8o o < . B [ . <+ Laf SIWIL € MNVL MOTIH3N0 omom:_n_ _ o <1 | I @ Eg 3NIT H3dWYS a39Hnd = ES N P4 W| . | ] 2 =20 . o S mm : + |1 . - . ad . . 1) MO14 §3788N8 1SNNQY B o ! o o __. " ONIL31HQ MOTd ¥378d9nd§ °, . © - oJ hd N [ ol L] H L] O N aJ g . » STNIL € INIT MOTIHIAO Q3o8Nd | . o~ -o @ uw ¢ 440 dWnd_,. 1" (NOILYNIWVLNOD ON) oz:0moxu ) aw = o e * ) w B—' e, oS "M.o.a... 0a.®" ‘ %q LX) ........,...... aw ..'l.c...ooo.o........... i Theten, ooo.-o"..'.'uuolo.'.o ® 0040000000000 0, o > - , s "% ..ool..........r 10%: - : : 0 ; 10 - 20 30 _ 40 50 60 70 80 90 100 150 120 130 140 150 TIME AFTER 85Kr FLOW TURNED GFF (hr) - Fig. 8. Results of Krypton Experiment Run 3. LT COUNT RATE (counts/min) 18 ORNL-DWG 67-1960 5 v ALL COUNT RATES CORRECTED FOR DEAD TIME * ALL COUNT RATES CONVERTED TO MONITOR B3 READINGS . STAGNANT OVERFLOW LINE AND SAMPLER LINE WERE PURGED WITH * : CLEAN He BEFORE &°Kr FLOW WAS TURNED OFF . PUMP BOWL LEVEL 61% 2 Py L] . L ] 109 . L ] hd w . =2 0 3 - 5 5 . ff.j : : .. q wy * [a) b = » < L] w . =z 2 .: 5 ., g .'. ':LJ - : 4 * > 10 o 2 (N [m] ~~. o e, . % ® Seee . . o . 5 H L .‘ . L . . [] - . . . ) . . | ® 0 30 60 90 120 150 180 210 240 270 300 TIME AFTER 83Kr FLOW TURNED OFF (min) Fig. 9. Results of Krypton Experiment Run 4. ANAIYSIS OF THE &°Kr EXPERIMENT General Approach Analysis of the 8°Kr experiment is concerned with the stripping phase of the runs. The principal stripping processes involved, in order of occurrence, are purging the pump bowl, stripping the salt and asso- ciated circulating bubbles (if present), and then leaching the graphite. Other leaching processes of no fundamental interest but of importance because they contribute to the measured flux decay curve are diffusion out of the stagnant bubbler kidney described earlier and leaching 8 5y that may have been trapped in gas pockets located in the primary loop. Locations of potential gas pockets in the loop are in the freeze flanges, graphite access port,.and the spaces formed by the assembly of the core &y 0 COUNT RATE (counts/min) o o &) " ORNL-DWG 67-1961 TIME AFTER ®5Kr FLOW TURNED OFF (min) Fig. 10. Results of Krypton Experiment Run 5. [, ALL COUNT_ RATES CbRRECTED FOR DEAD TIME ALL COUNT RATES CONVERTED TO MONITOR B3 READINGS > STAGNANT OVERFLOW LINE AND SAMPLER LINE WERE PURGED WITH * CLEAN He BEFORE 85Kr FLOW WAS TURNED OFF —* PUMP BOWL LEVEL 70% ~ 'o . . . Y . \ .| o. 5 ., —J . a LY - s bt oy b 2 '.O.-... < - (n_'g .....lo.......'.. E (XN ] ®e g0 ssgle + . * * . e__e e * | * * . . ’ ) . . 0 30 60 S0 120 150 180 210 240 270 300 330 360 390 420 6T ORNL-D‘WG 67-1962 . ALL COUNT RATES CORRECTED FOR DEAD TIME . ALL COUNT RATES CONVERTED TO MONITOR B3 READINGS I |’ STAGNANT OVERFLOW LINE AND SAMPLER LINE WERE PURGED WITH " CLEAN He BEFORE 83Kr FLOW WAS TURNED OFF . PUMP BOWL LEVEL 555% L ] R [ ] L ] .. [ ] —— [ ] c - E N S~ w . = . 3 . 3 L ] w ° = . q L ] o (Y E 2 % =} ] o ° Q ‘\ \ 104 \b, o .~.‘~0 oo se o .. [ ] 5 v e T ~ 8 ® - ! [ ] L) * . - . . L ] . , | ‘ o} 50 100 150 200 250 300 - 350 400 . 450 500 550 TIME AFTER 85Kr FLOW TURNED OFF (min} 600 Fig. 11. Results of Kry‘ptbn Experiment Run 6. 3 650 700 €] Oc ‘\ . » ) 21 blocks. - There are various bits of evidence that pockets actually exist, although their location and capacity are not certain.. .The fuel salt circuit time around the loop is 25 sec, which is short compared with-the time scale of the stripping process involved, so the fuel loop can be considered as a well-stirred pot. At any Specific time therefore,-the-kryptbn concentration is considered to be constant through- out- the loop.‘ In the simplest case, it can be shown that each transient stripping process, when unaffected by any other stripping process, will .obey an exponential decay law; that is at time t, —Qt Kr flux, = Kr flux_ e : t In the actual case, however, each stripping process will affect every other stripping process to a greater or iessér extent. Note that pump bowl purging, salt stripbing, and graphite leaching are series processes; that is, they occur in the sequence given; while leachings of the several graphite regions are barallel processes; that is, they occur simulta- neously after the krypton concentration in the salt starts to drop. Quali- " tatively, the measured decay curve would be expected to be the sum of the contributions of each leaching process, as shown in Fig. 12. Note that ORNL-DWG 67-1963 CUMULATIVE Kr FLUX FROM REACTOR _PURGING Kr IN PUMP BOWL STRIPPING Kr IN SALT LOG COUNT RATE (counts/min) TIME - Fig. 12. Qalitative Breakdown of Cumulative Flux Decay Curve into Its Components. ' ' 22 the count rate in the off-gas line is plotted on the ordinate and is a unit of concentration; however, since the off-gas 1is fiowing at a con- stant rate, it also represents the 85Ky flux leaving the reactor. Each of the component curves should approach an exponential decay after the initial transient. Now the problem is to separéte,these individuql processes from the measured flux turve, with the realization that there may be dther leach- ing processes not accounted for. It should be pointed out again that the breaking down of a single composite data curve into several individual processes and the determination of rate constants for each is quite com- Plex and necessarily subject to a certain amount of personal interpreta- tion.- Two approaches were used in analyzifig the data. The most success- ful method consisted of an exponential peeling technique, as shown quali- tatively in Fig. 13 for run 3. The assumption is made that the tail of the decay curve is determined completely by leaching the slow (bulk) rate constant graphite. The procedure was fhen to determine the equation for the slowest exponential that fit asymptotically on the curve and subtract it from the data. ‘The next exponential equation that fit asymptotically ORNL-DWG 67-1964 CUMULATIVE Kr FLUX FROM REACTOR STRIPPING Kr IN SALT PURGING Kr FROM PUMP BOWL —‘(-‘ Kr LEACHED FROM VARIOUS . ————————————— GRAPHITE REGIONS LOG COUNT RATE (counts/min) TIME Fig. 13. Actual Method Used to Break Down Cumulative Flux Decay Curve into Its Components. ' N 23 on the rémaining 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 be- cause of the 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 strippifig process starts at zero time and proceeds independently at all others. It will be geefi, however, that this approach is adequate for both the vefy slowest rate constant processes (leaching bulk graphite) and the very fastest rate constant processes (purging pump bowl), but it is inadequate for intermediate procesées (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 function only of the slopes of fhe exponentials involved, so abso- lute calibrations of the monitor and detailed knofiledge of the &%Kr con- centrations are not necessary. Numerical results of peeling run 3 and ‘their'intefpretation are given in Table 2. This approach to analyzing the data was the principal method used. It is of necessity confined to . the fastest and slowest rate processeé 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 attémpt to determine rate constants for the intermediate processés in- volved, 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 powl 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 successffil,_probably for the following reasons: , ' 1. There were actually more than five 8°Kr sources in the system, so the mathematipal'model.Was bverly simplified. Primarily the,effects of circulating bubbles were not adequately accounted for. COUNT RATE (counts/min) ORNL-DWG 67-1965 5 d 4 2 L ! 10 '\ 5 \ ¢ "hooooou.oo 2e®, .o L] [ 1 g o000 .... T Y rvrey - “q e o._.t..l0.oooou—"rr'o.oo-looouooo-......m cscee ] e L 'fl.&uoo.l.o.... 2 \ tyo =198 hr LI % o 3 \ 10 \ 1\ 1\ N 1\ N \ \s—t172 = 352 br ; \\ \ \ {'11/2 =155 hr 4 \,/\1,/2 =1039 hr \ 5 \\ t/p = 019 hr \ 10° . 0 10 20 30 40 50 60 TO 8O S0 100 1o 120 130 140 150 : TIME (bhr) Fig. 14. Results of Exponential Peeling of Krypton Experimerit Run 3. v e a0 25 Table 2. Numerical Results of Peeling Run 3 of Krypton Experiment Count-Rate Peeled-Curve Intercept at Half-Iife Rate Constant Process (hr) Zero Time Determined (counts/min) 198 . 3,574 \ Mass transfer to slow- Mass transfer coeffi- est rate constant cient (bulk) graphite 15.5 2,178 Mass transfer to next Mass transfer coeffi- faster rate constant cient graphite 4,52 2,114 {a) 1.039 4,945 (b) ‘ 0.119 520,000 Pump bowl purging Purging efficiency aProbably influenced mainly by mass transfer. to fast rate 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. 2+ The approach required accurate knowledge of the initial concen- tration of the krypton in all regions involved (boundary values). This could not be done for the graphite for reasons to be discussed later in the section oh Capacity Considerations. The results of the second method will not be presented here. Pump Bowl Dynamics Schematically the pump bowl can be represented as follows: Pump Bowl - 85y N Monitor He purge Vgp = Volume of gas phase Off-gas Q = ft3/hr at 1200°F Cg = Average °°Kr eoncen- ’ Avout | 1ine - 8P and 5 psig tration in gas phase 70°F | - fi : fi"- — Xe stripper spray ring ' S = Salt stripping efficiency Salt phase p . . 5/ = Bubble stripping efficiency Qgp = £t salt/nr C§ = 85Ky concentration in ' salt Salt back to _ ) loop Void fraction 1l 26 [ 73 The dilution of 8°Kr in the gas phase of the pump bowl is given by* K dc Q_E Q.S Q. 8’ & .8 Kk, sp Kk, Sp Kk dt v Vv Vv B gp P ep In the first term Cz is the mean ®°Kr concentration in the gas phase of the pump bowl and the product Ec: is the concentration in the off-gas 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 krypton is stripped from the circulating bubbles, where | is the void fraction and S’/ is the bubble stripping efficieficy. If these three terms are evalfiated 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 ¥ and S/. It must be neglected because of inade- quate 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 k acC E ._gz_EEP_Ck dt v g’ gp and, solving for Cg at time t, gives - E/V - )t Kk (QgpB/ V) g £0 ? which, evaluated at concentratioh half-life conditions, is *See Appendix D for nomenclature. 2'7 ) g 1/2 = e_(QgPE/VéP)tl/z _ ,0.693 or, solving for‘E, 0.693V E tl/EQgp Figures 15 and 16 show the initial transients for runs 1 through 6. Since the bubbler line stagnant kidney and the salt stripping have little ORNL-DWG 67-1966 A RUN 1, HALF-LIFE OF CURVE = 6.8 min ® RUN 2, HALF-LIFE OF CURVE = 6.3 min O RUN 3, HALF-LIFE OF CURVE =83 min — | COUNT RATE (counts/min) TIME (min) Fig. 15. Expanded Plot of Data for the First Half Hour of Runs 1, . 2, and 3. All count rate data taken with monitor B4 and corrected for dead time. 28 ORNL-DWG 67-1967 104 A RUN 4, HALF-LIFE OF CURVE = 7.6 min ® RUN 5, HALF-LIFE OF CURVE = 6.3 min 0 RUN 6, HALF-LIFE OF CURVE = 8.4 min -6 fl : A 5 2 COUNT RATE (counts/min) 0 5 10 15 20 25 30 35 40 TIME (min) Fig. 16. Expanded Plot of Data for the First Half Hour of Runs 4, 5, and 6. All count rate data taken with monitor B4 and corrected for dead time. 29 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 7Q°F is identical to the reactor half-lives where | the operating temperature is 1200°F. 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 Indicated Pump Volume of Gas Half-Tife Pump Bowl Run Bowl Level at Phase in of Curve Purging No. Start of Strippin Pump Bowl . Efficiency (% scale) (£t3) (min) (%) 1 71 .75 6.8 6l 2 60 223 6.3 84 3 60 2.23 ' 8.3 64 4 61 2.19 7.6 68 5 70 . 1.79 6.3 67 6 55.5 C 2.43 8.4 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 moré or less consistent with those.measured at the University of Tennessee in a COjz- - water system, but the calculations are so approximate and dependent on hazy assumptions that they will 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%) that is characterized by salt velocities of about 0.7 ft/sec and a Réynolds number of about 1000. The mass transfer. coefficient will be between that for laminar and that for turbulent flofi. Second, there is the graphite associated with the centermost fuel chan- nels, which comprises about 1.5% of the graphite. The fuel velocity and the mass transfer coefficient in this region will be higher than in the bulk graphite region. Third, there is a region of structural graphite across the battom of the core. It is difficult to determine the exact boundary of this region, but it probably consists of approximately 3.5% of the graphite and is in a zone of low nuclear importance. It is char- acterized by orificing effects, impingement of salt, and fluid dynamic entrance regions; therefore it will ha&e the highest mass transfer coef- ficients. : ' ‘ _ g ‘The first question td be resolved concerns salt-to-graphite coupling via the mass transfer coefficient. The krypton flux from the' graphite can .be expressed as | Kr flux from graphite = hIiAG(Clgi - Cl;) 5 where Cgi is conventionally defined as the krypton concentration in the salt and at the interface, where the interface is continuous. In this case the salt-gas interfgce is inside a pore that occupies only a small fraction of the total graphite surface area. Therefore we neéd a rela- tionship between this concentration at the pore interface and the more conventional CEi' This is discussed in Appendix B, where it is shown that the mean concentration of krypton in a continuous salt film across the graphite surface is épproximately equal to the krypton concentration in the salt at the salt-gas interface inside a graphite pore. The rate at which €°Kr is ieached from the graphite is a function of several parameters; for instance, the diffusivity of krypton in graph- ite, the mass transfer coefficient, and the 85Kr concentration dissolved in the bulk sait, which is in turn a function of the xenon stripper effi- ciency. The general approach in the graphite analysis will be to first show that this rate is very insensitive to expected values of the dif- fusion coefficient of krypton in graphite. This being true, we can e 31 determine a relationship between the mass. transfer coefficient and the stripping efficiency, any combination of which will result in a flux curve as meesured. Thefi by weighting this.relationship'with’the value of strip- ping.efficiency measured at the University of Tennessee, theoretical velues for the mass transfer coefficient (see Appendix C), and other con- siderations, we will obtain a very narrow range of‘possible values for the mass transfer coefficient. Generally, this procedure will be fol- lowed for all the graphite regions considered. Most of the calculations wili be confined to run 3, which was concerned primarily with measuring graphite rate constants. Consider the ®°Kr flux from graphite as a function only of its in— ternal resistance (Dg) and its external resistance (pi). Also specify that, for times equal to or greater than zero, the krypton concentration dissolved in the fuel salt is zero. Cylindrical geometry is used; that is, each core block is considered to be a cylinder, the surface area of which is eqfial £b the fuel ehannel area aseociated with a single core block. The volume'of a graphite cylinder ef this sort is very close to the volume of the actual core blocks of the same length. The differen- tial equation that describes this case is G G G +__'='—k . dr? r Or Dy ot with Boundary conditions k .k - CG = CGO at t = 0, ack —[=0atr =0, dr de h_HRT G N ck at r=r dr Dk G b 32 The solution to this equation is ' ' k ok 'ch i -J;' Jl(Mn) —[(Mn)2DG/r€€:|t i r G Go o1 Mo Jg(Mh) N Ji(Mn) 0 ’ where the eigenfunction is and: where 7.ismthe eigenvalue. Now, differentiating with respect to r and evaluating at r = r , we have K k k g\ g, = J2(Mn) —[(Mn)zDG/rée:lt 2 ar ’ r, n=1 J5(Mn) + JZ(Mn) Flux == = — |— b € \dr Ty we obtain kk o 5 _[ sk 2] . 2DCos Jl(Mn) (Mn) DG/rbe t Flux, = —2 ) e : r 2 2 b r e n=1 J§(Mn) + Ji(Mn) From this équation 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 exponential being determined by the exponent of e. The problem now is one of relating these exponents to the slopes of the peeled - 33 flux curves. Considering run 3 it is obvious that the slowest exponent (t1/2 = 198 hr) is related to the bulk graphite, and it is expected that the next exponential (ti1,2 = 15.5 hr) is related to the graphite region located at the center line'of_the‘cofe. The next exponential (ti,z = 4.52 hr) has a fairly low order of confidence in equating it to any specific graphite region and will not be considered. It can be shown that for each of the two graphite regions considered, only the first térm of the above series is significant. Thérefore the exponent of e can be related to the measured half-life, as follows: - Now, by evaluating this equation in conjunction with the eigenfunction equation, we can relate values .of hm and Dk This was. done with the fol- lowing paramgter values, and the results agpear in Fig. 17: - t1/, (bulk graphite) = 198 hr (run 3), t1/2 (center-line graphite) = 15.5 hr (run 3), ¢ = 0.10, " - r, = 0.0905 ft, ) H = 8.5 X 107% moles/cc-atm, HRT = 6.43 X 107%. The ordinate represents the range in which»Dg is expected to lie. Note that for bulk graphite the value of hi is almost completely independent of Dé; therefore the mass transfer coefficient is controlling the krypton flux from this graphite region. For the center-line graphite region, the dependence of flux on Dg Dk GI becomes significant only at low values of It is difficult to extract hi information from run 2 because the time intervals involved were too short. The krypton addition and strip- ping phases were about 60 hr each..'During this relatively short addition time the bulk graphite reached only about 20% of its saturated value, in contrast to run 3, where it reached about 70% of its saturated value. For both runs the center-line graphite region (t1/2 = 15.5 hr in run 3) 3. ORNL-DWG 67-1968 1073 5 2 NEXT GRAPHITE REGION N AFTER BULK GRAPHITE z (CENTER-LINE REGION OF L, CORE) £ 10 } x (B | =] \ | i 5 \\ \ ? 2 | —BULK GRAPHITE 1075 5 ps 0 01 02 03 04 05 06 07 o8 h:‘noss (ft/hr) Fig. 17. Relationship Between D and hi That Fits Graphite Leaching Curves Peeled from Run 3. . ‘ was almost completely saturated. After stripping for 60 hr in run 2, the slope of fihe 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. Now, since hm is not a strong‘function of Dg, we can determine the relationship between hfi and S (stripping efficiency). This will be done for the bulk graphite region after sufficient time so that other tran- sients 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 Kr flux from xenon stripper = 8Q C 35 . kB k k Kr flux from graphite = h_ AG(CSi CS), | | ack Dilution rate of Kr in salt = -V —. S at Theh, substituting, k acC sq cf = nBa (ck - ~v =, Sp S m G si S S 4t In order to solve this equation, krypton concentrations must be converted to krypton fluxes because this is the formlof the data. The measured krypton flux is related to the stripping rate as follows: kK Flux = SQ,SPCS ’ and d flux dCi — = 3Q —_— at SP qat Rearranging gives Ck _ Flux . 2 S SQ,-Sp and dcg 1 d flux and now, confining ourselves to one graphite region, and specifically the bulk graphite from run 3 (t1,2 = 198 hr), it can be shown that Flux - Flux, ,—0-693t/t172 36 and d flux —0.693 flux 0 e—(0.693/t1/2)t dt - ti1/2 ’ Substituting into the above equations gives _ W% ~(0.693/t1/2)t and k ac; —0.693 flux, ~0.693/t1 /) dt SQ,Sptl/2 | Fufther, substituting these into the original rate balance we get ‘ fl Flug e (0+693/t1/2)t _ kB, [k _ ™o ~0.693/t1/5)t : 0 m G i sp - 0.693V flux N s 0 e-.(0.693/t1/2)t . S t QSP 1/2 . k. - Solving for CSi gives flux h A 0.693V ok of, ,m’e_ " s e—(0.693/t1/2)t si kB - ' ? S S t , hm AG | QSP ' QSP 1/2 and in its differential form, k kB dCy; —0.693 flux, . by Ag 0693V ~0.693/t1 /)t = 1{B ‘ 2 o S t @ Tt Ae \ Plp SOt which relates Czi and dczi/dt to the measured slope of the flux curve and the various physical parameters involved. At this point we will set up' a rate balance on the bulk graphite, as follows: Kr flux from graphite = dilution rate of Kr in graphite, 37 where , . _ kB k _ .k Kr flux from graphite = h_ AG(Csi Cs) s ack Dilution rate of Kr in graphite = — G Ti—t— R or . k kB dCq by Be /x K — . — ¢c.—C ’ dt VCT s1 S where Clé is the mean krypton concentration in the graphite. Now in the previous analysis it was shown that for the bulk graphite, hx}:lB‘is inde- pendent of Dlé sult is that the krypton concentration profile across a graphite core over. the range of interest. One consequence of this re- block is essentially flat. We can therefore say that k. k Ce = Cgi 2 and also, from Henry's law, Substituting this into the graphite ré.te,balance, we have k kB dc. h si _ hm AGI-IRIII (Ck _ Ck) dt eVG si s/ ' Substituting previously derived relations for Cls{i’ dC}sii/dt, and Clg into the above equation, and solving for hiB , we have, 0.693¢ ( O.693VS ) l — E————————— B AGHRTt Q 5 h _ 1/2 t1/2S S m 1 0.693 € 1 ’ —— + == V. T8¢t (HZRT VG) G Sp 1/2 38 We now evaluate hfi? as a function of S for the following values Qf other parameters: tl/2 = 198 hr (bulk graphite), . £ = OnlO, A = 1450 ft° (channel surface area in bulk graphite region), V, = 64.8 ft? (volume of graphite in bulk region), G vV, =70.5 £t° (volume of salt in loop), Q,Sp = ?O gpm, | H=28.5 x 10-° moles/cc-atm, . HRT = 6.43 x 1074, : | . The results of this calculation are shown in Fig. 18, where the mass trans- fer coefficient (hm) is plotted agalnst stripping efficiency (S). In . - this figure the superscript B refers to the bulk graphite region. Also shown on this plot is the theoretical expected range of hiBlbased on ORNL-DWG 67-1969 04 T I . ¥ 1 1 1 kCL SHADED AREA - EXPECTED REGION WHERE h*“t vs S CURVE SHOULD LIE FOR CENTER-LINE GRAPHITE 4 — / 7/ KkCL 0.3 “ 44— THEORETICAL h/’s FOR CENTER-LINE GRAPHITE ;% REGION IN TURBULENT FLOW é% ' { | o2 SHADED AREA - EXPECTED REGION WHERE htB vs. s_ CURVE SHOULD LIE FOR BULK GRAPHITE hX , MASS TRANSFER COEFFICIENT (ft/hr) 4 : | THEORETICAL h® FOR TURBULENT] ' | U7 FLOW FOR BULK GRAPHITE | - S T I OR 9/ 7 % THEORETICAL h® FOR LAMINAR . YN FLOW _FOR BULK GRAPHITE ~ -EXPECTED RANGE OF S .0 I I | O 10 20 30 40 50 6 70 80 90 100 S, STRIPPING EFFICIENCY (%) - ~ Fig. 18. Relatlonshlp Between hm and S for Bulk and Center-Line Graphite Regions. 39 laminar and turbulent flow; it displays the uncertainty in the diffusivity of krypton in salt. In addition the expected range of stripping effi- ciehcy is outlined. Note that the calculated curves fall within the ex- pected range. _ | In order to pick out more explicit values of th, we can weight this curve with the following two cons1deratlons. First, it is expected that some 01rculat1ng bubbles were present as will be shown in the next sec- tion on Capacity Considerations. Furthermore, it is expected that cir- - culating bubbles increase the effective stripping efficiency to the high end-of the indicated range, and'likely even higher. Second, most of the salt:iu the bulk graphite region is of a laminarrcharaoter, rather than turbulent, so h;? ought to be on the lower end of the‘expected range; Therefore, from Fig. 18 and with the above weighting considerations, we might pick out a probable range of hfi?'to bulk graphite as 0.05 < K < 0.09 £t /hr . The next graphite region (tl/é = 15.5 hr), interpreted as the center- line graphite region, is more difficult to handle. The previous deriva- tion assumes that all the krypton dissolved in salt comes from the graph- ite region under consideration. Now, when working with the center-line ‘region, we must also consider the krypton dissolved in salt that origi- nates in the buik graphite. "An equation whose derivation is similar to the above and which partially compensates for tlis is 0.693V>" BB G l + m G CL. oL L _ AChe] ) HRT QS - J m ‘ nEBaB 0.693ev° L AN m G G 1/2 9] 1+ - T L 1+ L, T a,S | Sty R 6, £luxg where the superscrlpts CL and B 1nd1cate center- llne and bulk graphite reglons, respectlvely The equatlon was evaluated w1th the same parame— ter values as before and with the follow1ng additional ones, and for a given value of S the value of hfi? was taken from the preV1ous calculation 40 for the same void fraction: tg?z = 15.5 hr (center-line graphite region), ACL = 14.5 £t? (channel surface area in center-line region), VgL = 0.682 ft> (volume of graphite in center-line region), Fluxg = 3574 counts/min (intercept of peeled curve at t = O fer bulk graphite), FluxgL = 2178 counts/min (intercept of peeled curve at t = O for bulk graphite). Th% results of this caig;latiop appear on Fig. 18. Also shown is the | theoretical range of hm based on turbulent flow and displaying the un- certainty in diffusivity of krypton in salt. The equation for hkCL is 1nvalld at low values of S because kkB approaches 1nf1n1ty, hence the llnes are terminated as they approach the equivalent line for th Nev- er?heless, 1t seems that a reasonable range of hkCL for the MSRE would be between 0.25 and 0.4 ft/hr. Capacity Considerations In addition to rate constant determinations from slopes of the peeled exponentials, we should be able to infegrate under the curves and deter- mine information on the capacity of the system. For instance, the inte- gral of the bulk graphite curve (t1/2 = 198 hr) should yield.the approxi- mate &Kr capacity of this graphite.. Then, from knowledge of the 8 5kr addition concentration, we could compute the‘approximate graphite void fraction available to krypton. When this calculation was performed with the.additioh concentration taken as the mean pump bowl concentration, _ the graphite void fraction came out to be about 0.40. This is obviously incorrect, even when' the rough nature of the calculation is considered. The reason for this is that kryp%on was added through a bubbler,'and it bubbled up through the salt at approximately one order of magnitude higher in concentration than in the pump bowl proper. These highly concentrated krypton bubbles were caught in the turbulent and recirculating zone formed by the spray ring. Very likely some of these bubbles, or micro bubbles, were carfied into the primary loofi and circulated with the salt. The re- sult was that the concentration of dissolved krypton in the fuel salt was . 41 much higher than it would have been based.on the mean pum@ bowl concen- tfation. Now, if we compute the graphite void fraction based on the dis- solved krypton in the salt being in equilibrium with the bubbler addi- tion 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 useful information on capacity 1is available from the data. It should be pointed out that the choice of a bubbler line for 85K; addition as opposed to the pressure reference leg, which’would not have given this deleterious effect, was dictated by other consider- ations. - XENON-135 POISONING IN THE MSRE General Discussion To calculate the'steady—staté'l35Xe poisoning in the MSRE, it is first necessary to compute the steady-state 135%e concentration dissolved in the salt. This is because the ?%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 éourCe and- sink rate terms involved. The most significanf of these terms and considerations involving them are discussed below. Dissolved Xenon Source Terms and Considerations 1. Xenon Direct from Fission. The 135%e generation rate direct from fission is about 0.3% per\fiissibn. 2. Xenon from Todine Decay. The *3°I generation rate is 6.1% per 135 ) Te- fission, either direct or from the decay of It in turn decays to 135¥e with & 6.68-hr half-life. The total ?°Xe generation rate is there- fore 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 prin- éipal 135%e source is from the decay of iodine and since the 1351 nalf- 42 life is long compared with the fuel-loop cycle time (25 sec), it will be assumed that 135Xe is generated homogeneously throughout the fuel loop. ‘3. Iodine and Tellurium Behavior. Since '2°I and '35Te are pre- cursors of 3%Xe, their chemistry is important. In this model it is as- sumed that both elements femain in solution as ions, and therefore will ‘not be removed from solution by the xenon stripper or diffusion into the grabhite. Concerning iodine, its thermodynamic properties indicate this 10 Recent evidence from the reactor also indicates this to to be true. be true. Some iodine has been found in thé off-gas system (but very lit- tle, if any,_1351), but this is due to the volatilization of the precur- sor tellurium. Since 135Te has such a short half-life (<0.5 min), very little of it will have a chance to volatilize; therefore this effect is neglected. It is also assumed for this model that iodine and tellurium will not be absorbed on any internal reactor surfaces, such as the con- tainment metal and graphite. Dissolved Xenon Sink Terms and Considerations 1. Xenon De¢ay. Xenon-135 decays with a half-life of 9.15 hr, and decay takes place throughout the entire fuel loop. 2. Xenon Burnup. Xenon-135 has a neutron absorption cross section 11 of 1.18 X 10° barns averaged over the MSRE neutron spectrum. 3. ZXenon Stripper Efficiency. As noted earlier, the efficiency of the xenon stripper was measured at the University of Tennessee with a COs-water systemg and confirmed later with an Oj-water system.12 Both tests were for a bubble-free system. The measured rate constants were then extrapolated to a xenon-salt system.? The stripping efficiency is defined as the percent of dissolved gas transferred’from the salt to the gas phase in passing through the xenon stripper spray system. In magni- tude it turns out to be between 8 and 15%. 4. Xenon Adsorption. Xenon is not adsorbed on graphite signifi- cantly at these temperatures, 3,14 and it is very wnlikely that it will be adsorbed on metal surfaces. ' 5. Xenon Migration to Graphite. The amount of xenon transferred to the graphite is a function of the mass transfer coefficient, diffusion coefficieht of xénon in graphite, and the burnup and decay rate on the 43 graphite. During manufacture, this graphité was impregnated éeveral times to obtain a low permeability. Diffusion experim.ents2 with a - single sam- ple of CGB graphite yielded a diffusion coefficient of xenon in helium at 1200°F and 20 psig of about 2.4 X 1075 cm?/sec (9.2 x 10-5 £t2/hr). This was measured in a single sample of graphite and may not be repre- | sentative of fhe reactor core; however, it will be seen later that the poison fraction in the MSRE is not é strong function of the diffusivity. As previously pointed out, the core grgphite_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 re- gion, 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 Migration to Circulating Bubbles. As will 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 7 1. The '3°Xe concentration dissolved in the fuel salt was assumed to be constant throughout the fuel loop. From the éomputed results it . can be shown to change less than 1%. 2. Tt was assumed that the 12°Xe isotope behaves independently of all other xenon isotopes present. " 3. The 13%%e 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 composed of 72 annular rings, ©/— Core - | Core- element Q¥ | N as shown below .HeH 44, Average values of parameters such as neutron flux, percent graphite, mass Itransfer coefficient, etc., were used for each ring. : 5. The reactor system was assumed to the isothermal at 1200°F. Consistent with all previous assumptions, the rate balance of 13°Xe dissolved in the fuel salt at steady state is the following: Generation rate = Decay rate in salt + burnup rate in salt + stripping rate + migration'rate to graphite + migration rate to circulating bubbles P where the units of each térm‘are ;35Xe atoms per unit time. ZFach term will now be considered Separately. Xenon-135 Generation Rate The total 13%Xe yield is 644% per fission. The'cérresponding 135xe generation rate is 5.44 x 10'° 1?Xe atoms per hour at 7.5 Mw. Xenon-135 Decay Rate in Salt The decay of 135%e dissolved in salt is represented as follows: 0.693V C~ S S Decay rate in salt = ) +X 1/2 Xenon-135 Burnup Rate in.Salt The burnup rate of 135%e dissolved in salt is expressed incrementally by dividing the core into the 72 elements described above and is as fol- lows: 72 : X X i t = . Burnup rate in sal eZl ¢2ea feVeCS Xenon-135 Stripping Rate Recalling that the stripping efficiency (S) is defined as the per- centage of 135%e transferred from salt to helium in passing through the 45 pump bowl stripper, the stripping rate is expressed as . _. X Strlpplng‘rate = Q,SPSCS . Xenon-135 Migration to Graphite Each graphite core block will be assumed to be éylindrical. This seems to be a good compromise between the true case and ease of computa- tioh. The surface-to-volume ratio for a cylinder is very close to the channel surface area-to-volume ratio of the actual core blocks. Diffu- sion of 1?°Xe inside cylindrical éore blocks at-steady state and with a sink term is as follows: Solving for the following boundary conditions % = finite at r = 0, x: X = CG CGi at r r o we obtain where 2 X X 6 - _X (¢2O_ +, 7\ )) '; - | Ib-= zero-order modified Bessel function of the first kind. . Differentiating and evaluating at r;, we have fdac : T (Br.) 4 =c.5_%__1__. dr Io(firl) The 135Xe flux in the graphite and at the surface (r = r;) is given by or, substituting the previous equation, we obtain .4 DG Il(Brl) . B—. 1 € IO(Brl) The 13%Xe flux can also be represented by Combining the last two equations by eliminating C and then solving fof X N Gi Fhmr;weoMmfll - 1 . hXCX m s 1 h;HRT I (Br) 1+ 9 X BD, Il(Brl) in units‘of 135%e atoms/hr-ftz. Because of the flux distributions, graph- ite 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 '3°Xe flux into the graphite, as follows: | 72 pfyvp o Migration rate to graphite = Z} me ees e=1 WS HRT I (B r ) 1 4+ fe 0' e 1 X 5e DG Ii(Berl) in wnits of *?°Xe atoms per hour, where 1l volume of core element, il graphite volume fraction at v, v e F . € Y fuel channel surface area-to-graphite volume ratio. 47 It is assumed that Y is constant throughout the core moderator region and has a value of 22.08 ft~l. Xenon-135 Migrafiion Rate to Circulating Bubbles The rate of *35Xe migration to the circulating bubbles is represented by Migration rate to bubbles = h A (c: - c¥, in units of '35Xe atoms per hour. The salt film is by far the control- ling resistance; therefore the 135%e concentration in the bubble is uni- form and at equilibrium with the concentration in the salt at the inter- face. Consequently the previous equation can be written as [ f Migration rate to bubbles = hpA_ @: - HRTC%) : At steady state the migration rate to the bubbles equals the rate that_135Xe is removed from the bubbles, therefore Migration rate to bubbles = Decay ratep + burnup rate_ + bubble stripping rate , B where ' X O.693VS¢CB Decay rate in bubbles = - ) ‘ t1/2 Bubble stripping rate = Qspws’Cg s 72 _ Burnup rate in bubbles = Z} ¢2e0xfevew0§ e=1 and the burnup rate of '2°Xe in the bubbles is handled the same as in the salt, that is, by dividing the core into 72 elements of volume and adding up the burnup in each element. Substituting the individual rate terms in the removal rate balance equation we get 48 | 0.693V yCy Migration rate to bubbles = - S P I's 72 ¢ X X X + / : ;ZL Q2eg fevech i QSPWS CB ’ Now, this equation may be solved simultaneously with the previous equation to eliminate CE. This results in hpAgCo - hBABHRT 0.693V y 72 -'———S—'+ZQO'XfV\JI+Q 1stl X 2e e e Sp tl/z e=1 Migration rate to bubbles = 1+ in units of '35Xe atoms per hour. Xenon~135 Concentration Dissolved in Salt The 135Xe 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 ¢° 72 S 8 5.44 x 109 = + X X t, Z; ¢2eg feVels /2 e=1 72 X X h™ YF V C + QS SC}S{ + E I}r{le e e s P e=1 h HRT I (8 r.) 1+ me 0 e 1 X fieDG Il(?erl) hgAgCy 4 . hBABHRT ‘ ? 1 + 0.693V_y 72 « —_— / -+ tx Q'SPIL[S Z ¢2eU fevew _ 1/2 e=1 where the units of each term are 135%e atoms per hour. 49 Xenon-135 Poisoning Calculations The xenon poisoning as obtained in this report is defined as the number of neutrons absorbed by 135%e over the number of neutrons (fast and thermal) absorbed by 235U and weighted according to neutron impor- tance;l5 it is expressed as a percentage. The weighting function is the adjoinfi flux. When considering the core incrementally it is given by 72 * ox | * Px GZ"]_ ¢2e¢2efevecs " Z © ¢2e 2€ e e G Z © ¢2e¢2 feV Wc ‘ u Z) (o 1 1e 1e 8% b ) £UC ggege e e S where the first term in the numerator is the rate dissolved '?7Xe is burned up, the second is the rate 135%e in the graphite is burned up, and the third is the rate 135¥e in the bubbles is burned up; all terms are weighted with the adjoint flux. Now, the term representing the rate 135%e in the graphite is burned up can be replaced by the 135%e flux into the graphite times the fraction burned, that is n* yv F ¢® ¢ o O‘QS X me e e s e 2ee e’ = W HRT I (B r ) \¢ o +A° me g €1 2c BeDG Il(Berl) : | With this substitution the poisoning of 135Xe in the MSRE can be computed. - The reactivity coefficient is related to the poisoning by a constant, which is a function only of the nuclear parameters} This has been evalu- ated’® and is (8k/x)* = —0.752 P* . Estimated '3°Xe Poisoning in the MSRE Without Circulating Bubbles With the equations given above, 135%e poisoning has been computed for the MSRE for a variety of conditions subject to the assumptions dis- ~cussed earlier. The procedure was to first solve for the steady-state 50 1é’!s}(e concentration dissolved in the salt, and then from this to compute the poisoning. A code was.set up to do these calculations on a computer. Thé neutron fluxes used were those reported in Ref. 15 and corrécted with more up to date information.'! Values of many parameters used are given in Appendix A, and others were taken from standard reference manuals. Nominal values of various important rate constants and other variables were chosen, and the variation of polson fraction with these parameters was computed. These nominal values may be interpreted as approximate expected values. The first case to be discussed will be the bubble-free situation. Then the case of circulating bubbles will be discussed. In the bubble-free case the following nominal values éf various pa- rameters were chosen: Available void fraction in graphite, € 0.10 Diffusion coefficient of Xe in graphite, 1 x 1074 DE, ft3 of void per hr per ft of graphite Mass transfer coefficient to bulk graph- 0.0600 ite, hXB, ft/hr Mass transfer coefficient to center-line 0.380 graphite, hfigL, ft/hr Stripping efficiency of spray ring, S, % 12 Reactor thermal power level, Mw 75 The pump bowl mixing efficiency was found to have a negligible effect and was not considered. A The results of the calculation are given in Figs. 19 and 20. Each plot shows the poisoning as a function of the parameter indicated, with all others being held constant at their nominal values. The circle in- dicates the nominal value. From these plots the following observations can be made. _ — , 1. For the bubble-free case, the 1?5Xe poisoning in the MSRE should be 1.3 to 1.5%. 2. Generally speaking the poisoning is a rather shallow function of all variabies plotted. DNote particularly the insensitivity of poison- ing to available graphite void (Fig. 20) and the diffusion coefficient (Fig. 20). The reason is that hz'controls the '?°Xe flux to the graph- ite. This could be an important economic consideration in future reactors 51 ORNL-DWG 67-1970° 3 2 © 2 =z zZ 2 pdd ___.--—'_'__ @ / . > [Ty] 2 (a) 0 - 0] 0.02 0.04 Q.06 008 ) 0.10 0.12 MASS TRANSFER COEFFICIENT - BULK GR‘_APHITE (€t/hr) 3 2 ) © 2 < z 2 o ] o (] g ald (#) 0 0 (OR 0.2 . 03 04 05 06 MASS TRANSFER COEFFICIENT - CENTER-LINE 'GRAPHIT.E (ft/hr} 3 & o 2 M Z Z & —_ o N o L ] a - \\ a1 —~—] o \_._ bl — | {c) 0 ) -0 10 20 30. 40 50 100 STRIPPING EFFICIENCY (%) Fig. 19. Predicted '?°Xe Poison Fraction in the MSRE Without Cir- culating Bubbles at 7.5 Mw(t). See body of report for values of other parameters, . 52 of this type. For .instance, if xenon poisoning is the only consideration, the permeability specifications may be rej;axed somewhat. Other numbers of interest are given below. For the nominal case, the 13%Xe distribution to 'its sink terms is ORNL-DWG 67-1971 2 S :ED 0 = 31 2 a QQ X (o) 0 0 0 5 10 15 20 AVAILABLE GRAPHITE VOID FRACTION (%) 3 g, , < =4 z / @ o/ 2 . g / % - - (#) ; 0 - 1 10 100 REACTOR THERMAL POWER LEVEL {(Mw) 3 2 o 2 = pd 3 o o] o > X 22 ) {¢) 0 10° 2 5 104 2 5 103 DIFFUSION COEFFICIENT OF Xe IN GRAPHITE (ffa/hr) Fig. 20. Predicted *°Xe Poison Fraction in the MSRE Without Cir- culating Bubbles at 7.5 Mw(t). See body of report for values of other parameters. ‘ : k 53 Decay in salt 3.4% Burnup in salt 0.9 Stripped from salt 31.0 Migration to graphite 64 .7 100.0% Of the 135Xe that migrates to the graphite, 52% is bufned up and 48% de- cays, averaged ovef the moderator region. Again, for the nominal case, 96.4% of the total poisoning is due to *?%Xe in the graphite and only 3.6% is due to the "?°Xe dissolved in the salt. Estimated 12%Xe Poisoning in the MSRE with Circulating Bubbles Xenon, and all noble_gases_for that matter, is extremely insolfible in molten salt. From the Henry's law constant, 2 c§ = 2.08 X 10~ cz at 1200°F where the units of concéntration'are xenon atoms per unit volume. A sim- ple calculation would show that with a circulating void fraction of 0.01 and the xenon in the liqfiid and gas phasesvin equilibrium, about 98% of the xenon present would be in the bubbles, or.if the void fraction is - 0.001, 83% of the xenon would be in the bubbles. We would therefore ex- pect that a small amount of circulating helifim bubbles would have a pro- nounced effect on *?°Xe poisoning. Circulating bubbles have been observed in the MSRE. The most sig? nificant indications come from "sudden pressure release tests." These experiments consist of slowly increasinglthe system pressure from 5 to 15 psig'and then suddenly ventiné“the pressure off. During the pressure release phase, the salt level in the pump bowl rises and the éontrol rods are withdrawn; both motions indicate that circulating bubbles are present. Void fractions can be computed from these tests that range from C to 0.03 | but are generally less than 0.0l. The reactor operational parameters thafi controi the void fraction are not completely understood, and it ap- pears fo be a quite complex phenomenon. For instance, the void fraction may be a function of how long the reactor has been operating. The bubble diameter is extremely difficult to estimate. The only direct source of information on this point is from a water loop used for 54 MSRE pump testing. In this loop the pump bowl is simulated with Plexiglas so that the water flow can be observed. The bubbles that migrated from the pump bowl into the pump suction could be seen and were about the size of a "pinpoint." For lack of any better measurement they were taken to be in the order of 0.010 in. in diameter. As will be seén, this is not a critical parameter in these calculations. Information in the literature on mass transfer to circulating bub- bles -is meager. Nevertheiess, from Refs. 16 through 19 and other sources, the.mass transfer coefficient was estimated to be in the range 1 to 4 ft/hr and practically independent of diameter. Again it turns out that this is not a crifical,paraMeter, even over this fourfold range. It is also assumed that the existence of circulating bubbles will have no ef- fect on the salt-to-graphite mass transfer coefficient. This is equiva- lent to saying that the circulating bubbles do not come in contact with the graphite in any significant quantities. A parameter thaf is quite critical is the bubble stripping effi- clency. This is defined as the.-percentage of 135%e enriched bubbles that burst in passing through the spray ring and are replaced with pure he- lium bubbles. At this time there is no good indication as to what this falue is. It is probably a complex parameter like the circulating-void fraction and depends on many reactor opefational variables. For lack of any better information, a nominal value was taken as 10%, because this is about the salt stripping efficienc&,.but it could just as easily be in the order of 100%. 4 - Xenon-135 poisoning has been computed for the following range of variables pertaining to circulating bubbles. Nominal Range Parameter ) Value Considered Mean circhlafing void volume 0-1.0 Mean bubble diameter, in. 0.0ld _ 0.005-0.020 Mean bubble mass transfer coeffi- 2.0 0.5-4.0 cient, ft/hr , | A Mean bubble stripping effi- 10 0—100 ciency, 55 / Again the nominal value can be interpreted as the expected value but with much less certainty than in the bubble-free case. All other parameters not pertaining to the bubbles were held cOfistant at the nominal value given for the bubble-free case. Figures 21 and 22 show the computed 135%e poisoning as a function of circulating void volume with other pa- rameters ranging as indicated. Parameters not listed on these plots were ORNL-DWG 67-1972 1.4 1.2 BUBBLE MASS TRANSFER ~ 10 COEFFICIENT g (ft/hr) - 9. 05 > . s 08 1.0 8 : £ o6 ' @ u)x ) ‘ R A \\Q\\ 0.2 {a) 0] " 0 0.25 0.50 075 1.00 1.25 MEAN BUBBLE CIRCULATING VOID (%) 1.4 (- ! 1.2. ;;5' 1.0 :_,'.; MEAN BUBBLE DIAMETER =2 (in) == 08 | § . 0.020 bl 0010 o > 0 g \ » T 04 F — \‘ . | 0.2 () . 0 0 025 ' 050 075 1.00 1.25 . MEAN BUBBLE CIRCULATING VOID (%) Fig. 21. Predicted 135¥e Poison Fraction in ‘th:e MSRE with Circu- lating Bubbles at 7.5 Mw(t). See body of report for values of other parameters. - ORNL-CWG 67-1973 BUBBLE STRIPPING EFFICIENCY (%) 0 | 35%e POISONING (%) \\ ~ I (o) —— 50 0 100 0 0.25 0.50 075 100 1.25 MEAN BUBBLE CIRCULATING VOID (%) 2 10 . NN Y S \-"-'--_ S — ~ | TOTAL —| _ 2 o 3 — ) BUBBLES Z 0t = : : GRAPHITE 3 7 12 7 e 5 <; Q > 5, N 0.01 [ e 5 e SALT — (6) O o1 02 03 04 05 06 07 08 09 10 i MEAN BUBBLE CIRCULATING VOID (%) ~ Fig. 22. Predicted 12°Xe Poison Fraction in the MSRE with Circu- lating Bubbles at 7.5 Mw(t). See body of report for values of other parameters. » held constant at their nominal values. From these figures, the following observations can be made: | 1. Circulating bubbles have a very pronounced effect on 3°Xe poi- soning, even at very low void percentages. 2. The '3%Xe 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 effi- ciency. [} 57 Figure 22 also shows the contribution of each system (salt, graph- ite, 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 fapidly increasing contribution to poisoning by the bubbles. In contrast to the bubble-free case in which the *2°Xe in the graphite is the greatest con- tribution to poisoning, the 135%¢ concentration of the salt is rapidly- reduced by the bubbles and is thus not available to the'grapfiite. At the time this report was written, there was no accurate knowledge of the extent of 2Xe poisoning. Preliminary values based on reactivity balances indicate it is in the range 0.3 to 0.4%. 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 esti- mate more accurately the circulating void fraction and to determine what operational variables affect it. An attempt will also be made to esti~ mate the bubble stripping efficiency, although this may be quite an elu- sive parametér to evaluate. Actually, the most recent information seemsk to indicate that the circulating void fraction (V) is in the order of 0.1 to 0.3% and the bubble stripping efficiency (S/).is in the range of 50 to 100%. Equipment is currently being built to measure 135%e poison fractions more accurately. CONCLUSIONS The analyses presented indicate the follOW1ng 1. A transient experlment such as the ®°Kr experiment can be useful in determining rate constants and other 1nformat10n for a complex process such as noble gas dynamics in the MSRE. There are serious limitations, however, and a detailed study should be made beforehand. 58 2. The krypfon'experiment indicated that mass transfer coefficients computed from heat-mass transfer analogies are quite good for tfie molten- salt poroungraphite system. : 3., If the MSRE could be operated bubble free, the computed 135%e poisoning would be 1.3 to 1.5% at 7.5 Mw. However, the reactor does not operate bubble free, so the poisoning should be considerably less. This results from the extreme insolubility of xenon in salt. When the model is modified to include circulating bubbles, the compfited values can be made to agree with preliminary measured values (0.3-0.4%) by adjusting bubble parameters used over reasonably expected ranges. It would seem therefore that the model does portray the physical ‘reactor. However, to prove this conclusively, we must have accurateAknowledge of thé bub- ble parameters, and with these calculate precisely the l?SXe poisoning. We think.thé model is quite representative of this system and can easily be extended to_éther fluid-fueled reaétors of this type. 4. This model should not be taken as final. For instance, it was assumed that iodine does not volatilize. If it is later determined that iodine does volatilizé, the model will have to be adjusted accordingly. s, The'circulating helium bubble concept should be considered se- riously as a 135%e removal mechanism in future molten-salt reactors. He- lium bubbles could be injected into the flowing salt at the core outlet and be removed with an in-line gas.separator some distance downstream. 6. Thé_insensitivity of 135%e poisoning to the graphite void frac- ‘tion and diffusion coefficient should be noted. This indicates that the tight specifications of these Variables for the sole purpose of lowering the 135%e poisoning might not be necessary. Considerable savings could be realized in future_reactors. This phenomenon occurred in thé MSRE be- cause the film coefficient is the controlling mechanism for transfer of l?5Xe to the graphite. Each future reactor concept would have to be studied in detail to assure that this was .still true before the above statement was applicable. 59 ACKNOWLEDGMENTS We are indebted to H. R. Brashear of the Instrumentation and Con- trols Division for designing, building, and calibrating the radiation detectors fised to monitor 85Kr, fo T. W. Kerlin of the Reactor Division for his assistance in the finsteady-state parameter evaluation used in the krypton experiment analysis, and to the members of the MSRE operatQ ing staff for assistance in preforming the kryptonkexperiment. 16. 60 % REFERENCES: R. C. Robertson, MSRE Design and Operation Report, Part I, Descrip- tion of Reactor System, USAEC Report ORNL-TM-728, Oak Ridge National Laboratory, January 1965. Oak Ridge National Laboratory, Reactor Chemistry Div. Ann. Progr. Rept. Jan. 31, 1965, USAEC Report ORNL-3789. Oak Ridge National Laboratory, Molten-Salt Reactor Program Semiann. Progr. Rept. July 31, 1964, USAEC Report ORNL-3708. F. F. Blankenship and A. Taboada, MSRE Design and Operation Report, Part IV, Chemistry and Materials, USAEC Report ORNI-TM-7/31, Oak Ridge National Laboratory (to be published). I. Spiewak, Xenon Transport in MSRE Graphite, Oak Ridge National Laboratory, unpublished internal report MSR-60-28, Nov. 2, 1960. G. M. Watson and R. B. Evans, III, Xenon Diffusion in Graphite: Ef- - fects of Xenon Absorption in Molten Salt Reactors Containing Graph- ite, Oak Ridge National Laboratory, unpublished internal document, Feh. 15, 1961. N H. S. Weber, Xenon Migration to the MSRE Graphite, Oak Rldge National Laboratory, unpublished internal document. J. R. Waggoner and F. N. Peebles, Stripping Rates of Carbon Dioxide from Water in Spray Type Liquid-Gas Contactors, University of Ten- nessee Report EM 65-3-1, March 1965. Ietter from F. N. Peebles to Dunlap Scott March 31, 1965, Subject: Converting Stripping Rates from COj-Water System to Xe-Salt System. F. F. Blankenship, B. J. Sturm, and R. F. Newton, Predictions Con- cerning Volatilization of Free Iodine from the MSRE, Oak Ridge Na- tional Laboratory, unpublished internal report MSR-60-4, Sept. 29, 1960. B. E. Prince, Qak Ridge National Laboratory, personal commmnication to authors. F. N. Peebles, University of Tennessee, personal communlcatlon to authors. F. J. Salzano and A. M. Eshaya, Sorption of Xenon in High Density Graphite at High Temperatures, Nucl. Sci Eng., 12: 1-3 (1962). M. C. Cannon et al., Adsorption of Xenon and Argon on Graphite, Nucl. Sci. Eng., 12: 49 (1962). P. N. Haubenreich et al., MSRE Design and Operation Report, Part III, Nuclear Analysis, USAEC Report ORNL-TM-730, Oak Ridge National Labo- ratory, Feb. 3, 1964. E. Ruckenstein, On Mass Transfer in the Continuous Phase from Spheri- cal Bubbles or Drops, Chem. Eng. Sci., 19: 131-146 (1964). 17. 18. 19. 20. 21, 61 Li et al., Unsteady State Mass Transfer For Gas Bubbles — Liquid Phase Controlling, Amer. Inst. Chem. Engrs. J., 11(4): 581-587 (July 1965). P. Harriott, Mass Transfer to Particles, Part I — Suspended in Agi- tated Tanks; Part II — Suspended in a Pipeline, Amer. Inst. Chem. Engrs. J., 8(1): 93-102 (March 1962). S. Sideman et al., Mass Transfer in Gas-Liquid Contacting Systems, Ind. Eng. Chem., 58(7): 3247 (July 1966). . R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 1960. C. V. Chester, Oak Ridge National Laboratory, personal communication to authors. .mr_ , i M % etk e v 63 APPENDICES R S— N > 65 Appendix A MSRE PARAMETERS General Normal thermal power level, Mw Nominal operating temperature, °F Operating.pressure in pump bowl, psig Fuel salt flow rate, gpm Fuel salt volume, ft3 Graphite volume, ft3 Xenon stripper flow rate (estimated), gpm Salt flow along shaft to pump bowl, gpm Total bypass flow (sum of above), gpm Fuel loop circuit time, sec Graphite Grade ) Bulk dénsity, g/cm3 Porosity, accessible to kerbsene; % Porosity, theoretical, % Porosity, available to xenon and kryptom,* % Fuel salt absorption at 150 psig (confined to surface), % Wettability Graphite surface area in fuel channels, £t ; Diffusivity of Kr at 1200°F in graphite (filled with He), Kr atoms/hr.ft graphite (Kr atoms/ft’ gas) Diffusivity of Xe at 1200°F .in graphite (filled with He), Xe atoms/hr.ft graphite (Xe atoms/ft’ gas) Equivalent diameter of fuel channels in bulk graephite, ft Fuel Salt Liquidus temperature, °F Density at 1200°F, 1b/ft> Viscosity at 1200°F, 1b/ftshr Diffusivify of Kr at 1200°F (based on several estimated values), ftz/hr Diffusivity of Xe at 1200°F (based on several estimated values), ft2/nr Henry's law constant for Kr at 1200°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. : . T . Not wet by fuel salt at operating conditions. CGB 1.82-1.87 4.0 17.7 ~10 0.20 + 1520 ~1.0 x 107% ~0.92 x 1074 ¢.0519 840 130 18 4.3 x 107°=7.0 x 1077 3.9 x 107%=6.4 x 10~° 8 x 1079-9 x 10-° 2.75 x 107° 66 Appendix B SALT-TO-GRAPHITE COUPLING A question exists concerning the process of mass transfer from a fluid to a porous medium as opposed to a continuous or homogeneous me- dium. For example, the krypton flux from graphite to salt is given by k ' .k (k _ Flux~ = h A, (C., — C v where A, is the total channel surface area of the graphite. G hk is defined so that Ck m sf k) S The term is not the krypton concentration in salt at the salt-gas phase interface (located at a pore opening), but rather is some continuous concentration across the entire surface of the graphite. This is shown schematically below and would be similar for fhe case of xefion flowing from salt to graphite. Direction of Kr Flow P — — ' ' Boundary Layer A2 Flowing Salt (ck) Salt-Gas Phase Interface (Cgi Region of Conventional Mass Transfer %, ) "™ schematic Pore Contalnlng He and Kr _ Where hfi Is Applicable Equal Kr Concentration Profile (Ckf) In this region Kr is transported from the pore interface to the equal con- ! centration layer by a process of pure diffusion //j:;;;E;EEEj;// Schematlc G%gphlte Matrix //C/(////,/ / 7/ e 10{ — —— — ——— d— —— — — c—— A — —— 67 The mean pore entrance diameter for CGB graphite.isvless than O.1 H . and probably closer to 0.02 i, which is extremely small compared with the boundary layer thickness. It seems reasonable, therefore, that krypton -is transported from the pore opening to the contihuous concentration layer by a process of pure diffusion. Then from the continuous layer to the bulk salt, krypton will be transported by‘conventional fluid dynamic mass transfer. Note that since salt will not wet graphite, and because of the small pore size, the salt-gas interface will certainly not peqetrate inside a pore. Also inherent in this analysis is the idea that salt will tofich the solid graphite matrix, even though it .will not.wet it, and therefore the salt-gas phése interface will exist only at the pore open- ing. In order to couple the salt to the graphite, it is necessary to k Actually it will be shown develop a relationship between Cgf and Csi' that Ck. N,Ck . si sf | o In this development we consider a simplification of the previous figure, as follows: Boundary Layer Voo 7, k r. . r i s . f -y Unit Transfer 1 (L Interface Cell \ ~=——- Pore -l T R ‘ Ei;// . 2 ; . Csf \ Cor 7/—// P ‘The pure diffusion region\@Ssociatéd with a single graphite pore is ap- proximated in spherical geometry. The inner hemisphere at constant con- centration Cii,and radius r. is the source for krypton that diffuses- _through salt to the outer hemisphere at constant concentration sz and 68 radius rf.' Associated with each pore is a unit transfer cell of cross- sectional area WT%, thrbugh which krypton is transferred by conventional mass trans?er from the position of Cgf to thg bulk salt at condéntration Cg. The term r. is taken as half the mean pore entrance diameter and ro 1s related to it with the graphite void fraction. The general equation for diffusion in spherical coordinates at steady state, and ‘when concentration is a function only of the radius, is 2 d Ck 2 de S S +=—— =0 . dr? r dr t Solving with boundary values, as discussed above, Yy ¢~ o, == S si T kK k r. | Csf Csi 1 —-;i | i Differentiating with respect to r, ack r, cf - cF _ i st si dr 2 Ir. rT _.;l f k. dcls{, Flux = —DYA r S Tr dr gives S e Flux = —D'a —= Sf 81 r r o2 r, l—— r 69 Then, solving at r = ), we obtain r. for a hemisphere (Ar = 2wr§ k Cif - Cii Flux = —27r T i’s Ty _ l_I‘— f Without going into the considerations, we will state that a reasonable relationship between r. and ra is Substituting this into the equation for flux gives (E)¥/2 Fl1 —2wrka E (l( k‘) e S 1/2 st si c - 1"(3) Now, at steady state, this diffusion flux at r_, must equal the convective flux through the unit cell, where f .k : k K . Fluxunit cell hmAunit cell chf Cs) ¢ or o k(k _ k) Flu'xu.nit cell thm(csf Cs ) Therefore, equating fluxr and fluxunit cell’ vC obtain f k k k . fe\/? , Csf —'Cs 2Ds (3) k - k k 1/2 ) Csi Csf rfhm_l - (%) Solving for the following parameter values, 70 DS = 4.26 x 107° £t2/hr, h% = 0.06 ft/hr (approximate for bulk graphite region), r; = 0.1 u (actually probably closer to 0.02 i), € = 0.10, ' r. = 0.446 1, we obtain sz "C: * P k. —¢ which says that,the'concentration difference between Cgi and Cgf is neg- ligible compared with the difference between CK, and C¥. Another way of putting it is that Cgi ] Cgf. The equation at the beginning of this ap- pendix can now be written & 71 Appendix C THEORETICAL MASS TRANSFER COEFFICIENTS Theoretical mass transfer coefficients between fuel salt and graph- ite may be estimated by using standard heat transfer coefficient. relation- 20 These conversions ships and the analogy between heat and mass transfer. are brought about by substitution of equivalent groups from the following table into the appropriate heat transfer coefficient relationship. They apply for either laminar or turbulent flow. Heat Transfer Mass Transfer Quantity - Quantity pd v pd Vv Re = B =g O ) o) 73 Appendix D NOMENCLATURE Definition Sfirface érea Noble gas concentration. , Noble gas concentration in gas phase Noble gas concentration in.gréphité‘xl | Noble gas concefitration in salt Heat capacity Equivalent diameter of flow -channel Diffusivity . Pump bowl purging efficiency Void fraction of graphite Volume fraction of salt in element'Ve Volume fraction of graphite in element Vg Neutron flux Henry's law constant for salt Heat transfer coefficient ‘Mass transfer coefficient Modified Bessel functions of the first kind Bessel functions of the first kind Thermal conductivity Lehgth of fuel channel Radioactive decay constant Poisoning Volumetric flow rate Volumetric flow rate of helium at 1200°F and 5 psig through pump bowl Volumetric flow rate of salt through xenon stripper - Radius Radius at equivalent core block in cylin- drical geometry " Units a1 atoms/ft3 atoms/ft3 .atoms/ft3 atoms/ft3 Btu/lb-°F £t ft2/hr % neutrons/cmz-sec moles/cc-atm Btu/hr.ft2.°F ft/hr Btu/hr.ft.°F £t ' Term ta o ™ S/ * 2 K® X T4 Definition Universal gas constant Density of salt Stripping efficiency, defined as the per- centage of dissolved gas transferred from liquid to gas vhase as salt is sprayed through the xenon stripper Bubble stripping efficiency, defined as the percentage of 1*?°Xe containing bub- bles that burst in passing through the stripper and are replaced with pure heljum bubbles. Absorption cross section Time Half-1ife Absolute temperature Fluid velocity Volume of salt in primary lodfi Vblume of graphite in core Volume at gas phase in pump bowl Vélume of core element & . Aibitrary constant ‘Viscosity Ratio of fuel channel surface area to graphite volume in core Average void fraction of helium bubbles circulating with salt in primary loop Superscripts 135Xe Adjoint flux Mean Bulk graphite region Center-line graphite region Units cc.atm/°K-mole 1b/ft3 % barns 75 Subscripts Fast neutrons Thermal neutrons Boundary Circulating bubbles Element of core volume _ ‘Film Gas phase Graphite Heat Interfacé Mass Initial conditions Pump bowl At radius f Salt phase L T » T L (] ORI NEC I T S 76. 7. 78. 79-80. 81-358. ORNL-4069 ‘UC-80 — Reactor Technology Internal Distribution C. F. Baes, Jr. 27. R. E. MacPherson S. J. Ball 28. A. P. Malinauskas W. P. Barthold 29. C. D. Martin, Jr. S. E. Beall 30, H. A. Mclain N 'F. F. Blankenship 31. C. E. Miller, Jr. E. G. Bohlmann 32. A. M. Perry H. R. Brashear 33. M. W. Rosenthal W. L. Carter 34, A. W. Savolainen C. E. Center (K-25) 35=%40. Dunlap Scott E. L. Compere , 41. M. J. Skinner W. H. Cook 42. R. E. Thoma F. L. Culler ‘ 43. A. M. Weinberg J. R. Engel 44y M. E. Whatley / R. J. Kedl 4547, Central Research Library G. W. Keilholtz 48=49, Y-12 Document Reference Section T. S. Kress 50—74. Laboratory Records Department C. E. Larson (K-25) 75. Laboratory Records, RC H. G. MacPherson | : ~ External Distribution A. Giambusso, AEC, Washington T. W. McIntosh, AEC, Washington Division of Research and Development, AEC, ORO Reactor Division, AEC, ORO Given distribution as shown in TID-4500 under Reactor Technology Category (25 copies — CFSTI) c