operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION OAK RIDGE NATIONAL LABORATORY ORNL- TM- 730 MSRE DESIGN AND OPERATIONS REPORT PART [1l. NUCLEAR ANALYSIS . R. Engel E. Prince . C. Claiborne +* . N. Haubenreich T o0 NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use ot the Oak Ridge National Laboratory. It is subject to revisien or correction and therefore does not represent a final report. The information is not to be abstracted, reprinted or otherwise given public dis- semination without the approval of the ORNL patent branch, Lagal ond Infor- mation Control Department. /o0 LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United States, ror the Commission, nor any person acting on behalf of the Commission: A. Mckes any warranty or representotion, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, methed, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report, As used in the above, ‘‘person acting on behalf of the Commission' includes any employee o cantractor of tha Commission, of emplayee of such contractor, to the extent that such employee or contracter of the Commission, or employes of such contractor prepares, disseminotes, or provides access to, any informotion pursuant to his employment or contract with the Commission, or his employment with such controctor, wi ORNL TM-730 Contract No. W-7405-eng-26 MSRE DESIGN AND OPERATIONS REPORT PART ITT. NUCLEAR ANALYSIS P. N. Haubenreich Je« R. Engel B. E. Prince H. C. Claiborne DATE TISSUED FEB -3 1364 OAK RIDGE NATTICNAL. LABORATORY Ogk Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSICN ™1 iii PREFACE This report is one of a series of reports that describe the design and operation of the Molten-Salt Reactor Experiment. All the reports are listed below. The design and safety analysis reports (ORNL TM-728 and ORNL TM-732) should be issued by spring of 1964, and the others should be issued in the summer of 1964. ORNL TM~728 MSRE Design and Operations Report, Part I, Description of Reactor Design, by R. C. Robertson. ORNL TM-729 MSRE Design and Operations Report, Part II, Nuclear and Process Instrumentation, by J. R. Tallackson., ORNL TM-730% MSRE Design and Operations Report, Part III, Nuclear Analysis, by P. N. Haubenreich and J. R. Engel. ORNL TM-731 MSRE Design and Operations Report, Part IV, Chemistry and Materials, by F. ¥F. Blankenship and A. Taboada. ORNL TM-732 MSRE Design and Operations Report, Part V, Safety Anal- ysis Report, by S. E. Beall. ORNL TM-733 MSRE Design and Operations Report, Part VI, Operating Limits, by 5. E. Beall. ** MSRE Design and Operations Report, Part VII, Fuel Han- dling and Processing Plant, by R. B. Lindauer. ** MSRE Design and Operations Report, Part VIII, Operating Procedures, by R. H. Guymon, *x MSRE Design and Operations Report, Part IX, Safety Pro- cedures and Emergency Plans, by R. H. Guymon, *K MSRE Design and Operations Report, Part X, Maintenance Equipment and Procedures, by E. C. Hise. *% MSRE Design and Operations Report, Part XI, Test Program, by R. H. Guymon and P. N. Haubenreich. *% MSKE Design and Operations Report, Part XII, lists: Drawings, Specifications, Line Schedules, Instrument Tabulations (Vols 1 and 2). ¥Tssued., *¥These reports will be the last in the series to be published; re- port numbers will be given them at that time. CONTENTS Preface oo iiervenrenesrtnoasonees cestarannen Cesiersscessatsaavss e iii Abstract cevvievenan cesesssacs teereens seesenesassertessataanssatas e 1 1. INTRODUCTION eeonvsvnnoncoss thesesanen cereaseesues coeeresuns ceas 3 2. PRELIMINARY STUDIES OF CORE PARAMETERS «vvevesns et e reeenenaen 4 2.l Introduction cesvesesesssessssrosssnssansesas corevevresn s . Y 2.2 Effect of Core Size cvvevrnens creerereseeses Cresrsanranens 4 2.3 Effect of Volume Fraction in One-Region COTe€S .veeevesssn . 5 2.3.1 First Study seeeeeses Cresersaasseans Chresiersaenaas 5 2.3.2 Second StUAY veeeserensscsvennnas Cereeace e 8 2.4 Two- and Three-Region COTeES .uiievssssssnnssos it cseneanns 9 2.4.1 Channeled Graphite COreés .uieecessserscssvesssenses 9 2.4.2 Cores with Moderator in Reflector and Island ...... 12 2.5 Cores Containing INOR-8 Tubes ...u... Ce it esaacaeenaaane 13 2.6 CONClLUSLIONS tevvesnerscassssscacnsssssnsssssosssnsansonsesse 13 3. CRITICALITY, FLUX DISTRIBUTIONS, AND REACTIVITY COEFFICIENTS tvvvecovensasens ceeeseseanns PP 15 3.1 Descripbtion Of COre sieieeertesesesescsssessnnsssonsssassness 15 3.2 Calculational Model Of COTE tieensnscersssnssssssssssnssnns 15 3.3 Fuel Properties .veeeereccans . Cre e s et eseraesa et e 20 3.4 Cross Sections and Effects of InhomOgenelty of Core ...... 20 3.4.1 Resonance Neubtrons ..eeses. Cieecestartiassssnatesas 21 3.4.,2 Thermal Neublrons .iiveessssssssceasoas cheieeaneans . 22 3.5 Criticality Calculations ...... Creereaseareses cecesarresns 23 3.6 Flux and Fission Distribufions iveeiieriiecrssnsrsoccnssoccses 25 3.6.1 Spatial Distribution ...... testaean e e Ceessenssens 25 3.6.2 Energy Distribulion sieeveessecrsossescsarsssranannas 34 3.7 Reactivity Effects of Nonuniform Temperature ...cevececess 37 3.7.1 One-Region Model ..uiiicesecerseenescnossssssonononss 37 3.7.2 Multiregion Model ...ieeieietssssssassssseasasaonnans 41 3.8 Reactivity Effects of Changes in Densities of Fuel Salt and Graphite sevsesesovasesnssasscsasassssasessssnns 48 3.9 Summary of Nuclear Characteristics tiveeieerecssocsasscsss 49 4, CONTROL ROD CALCULATTONS . iuivereeerononeosseearsassannsnonanas 53 4.1 Control Rod Geomelry viveeveeeeeceesssscannns Ceacerriseaans 53 4.2 Method of Calculation of Rod React1v1ty tesessaasannereann 53 4.2,1 Total Worth seeeeeieennsnons cereas cesesteanaas cenen 53 4.2.2 Differential Worth c.ievecececas Ceeseesesteanasreans 57 4.3 Results of Calculations ..veeesecss Ceesesreserecseeserean . 58 4.,3.1 Total Reactivity Worth ...... Cerersaas et ecretreens 58 4.3.2 Differential Worth ..ieeeeeeeeenenertocacesssscssncas 58 5. CORE TEMPERATURE |, ,.....cecveevnenens cereseeas ceesenereasans vos 60 5.1 Overall Temperature Distributions at Power .isieesceesoesns 60 5.1.1 Reactor RegioOns sieeeeses Cetetisessessaseateas teaas 60 10. 5‘2 5.3 vi 5.1.2 Fuel Temperatures .eeeeveess 5.1,3 Graphite Temperatures ....... Average Temperatures at Power ..... 5.2.1 Bulk Average Temperatures 5.2.2 Nuclear Average Temperatures *» ® 0 Power Coefficient of Reactivity ...... DELAYED NEUTRONS «veeesosnserocsscasnsns 6.1 Method of Calculation seeesecesssoses . 6.2 Data Used in Computaltion .eieerecreccnscnnes 6.2.1 Precursor Yields and Half-Lives ..... 6.2.2 Neutron ERErgiesS teeeessscescosses 5423 AEE tiieersenrasesotscttirssanssesatorens 6.2.4 MSRE DImensions eeeseeecsccsssesssonsrsns 6.3 Results of Computation s.eeeerecsconesnsns 6.4 Nomenclature for Delayed Neutron Calculations POISONING DUE TO XENON-135 ........ Ceceneanree 7.1 Distribution of Iodine and Xenon .eesceees 7.2 Sources of Todine and Xenon Remova_. of Iodine and Xenon Sources of Todine and Xenon Removal of Todine and Xenon ~3 -2 -2 =1 ~1 2 H o oyt W in Fuel " & 0 8 » from Fuel in Graphite from Graphite .. Detailed Calculations eseeeeeeees Approximate Analysis «.... .o Reactivity Effects of Xenon-135 ....... POISONING DUE TO OTHER FISSION PRODUCTS 8.1 Samerium-14%9 and Other High-Cross-Section Poisons 8.2 EMPLOYMENT OF CONTROL RODS IN OPERATION +eveeenn. Low~Cross-Section PoisONs veeesvses General Considerations Shim Requilrements Shutdown Margins cieseceeveses 2 & % ¢ 8 & 4 4 8 880 0 * 9 % % 8 s &8 e & 8 4 ® 5 4 5 8 B 0 ® 0 &P YR DL . 8 e 08 ¢« & & 5" s o 85 0o s & & 00 * 88 » & Typical Sequence of Operations seeseeveerecrecccenocsnnes NEUTRON SOURCES AND SUBCRITICAL OPERATION seeveecvsrococeces 10.1 10.2 10.3 Intreoduction Internal Neutbtron SOUrCeS seseses s 10,2.1 Spontaneocus Fission . ® B & 0 0 9P BB B A S EE SN "8 P B OB ® & & 8 0 & v 8 0 10.2.2 Neutrons from (¢,n) Reactions in the Fuel ...... 10.2.3 Photoneutrons from the Fuel ceveeccessan Provisions for External Neutron Source and Neutron DeteCtOr'S veeeesncessssnsssnnsss 10.3.1 External SOUIrCE srseassoss . & 10.3.2 Neutron Detectors ceeeesess Neutron Flux in Subcritical Reactor ...... Requirements for Source .ieeeeven.s " e 8 & 5 4 0 s % 8 0 8 00 ® ¢ P e 0 s ® s & & S e . & % & 0 ¥ @ * R P 61 64 69 69 70 71 74 74 75 75 75 75 76 "6 78 81 81 81 82 82 82 83 84 85 20 90 91 96 96 97 98 98 100 100 100 100 100 101 105 105 105 106 109 11. 12. 13. vii 10.5.1 Reactor Safely iveeeveeeeerennns tressreena cesaen 10.5.2 Preliminary ExXperiments cvveeeeeseecsosscoonnnes 10.5.3 Routine Operation sesveeeseseecssscessssssaesons 10,6 Choice of EXternal SOUTCE tiveeereserorrosseasssserssns . KINETICS OF NORMAL OPERATION cveevveescansss seeresasersar s 11,1 Very Low POWET .siveeserrosvrensasns tesarsenoaaaranas N 11.2 Self-Regulation at Higher POWeTr tivvivritoeneasnonesennss 11.2.1 Coupling of Fuel and Graphite Temperatures cevee 11.2.2 Transport Lags and Thermal Inertia .cviveveesces 11.2.3 Simulator Studies teveeeessens tecernecanas cieeas 11.3 Operation with Servo Control .eiereeseosees cesssasanesas KINETICS TN ABNORMAL SITUATIONS — SAFETY CALCULATIONS civiven. 12.1 Introduction ssiiveveseesns escassestnes teterenscasans s 12.2 General Considerafions veeeeseeessssansenss crsesesseneas 12.3 TIncidents Leading to Reactivity Addition ..iveceveneenes 12.4 Methods Of ANalysSis seveesoesenreotoencacncnnns ¢reseesn 12.4,1 Reactivity-Pover Relatlons .................. oo 12.4.2 Power-Temperature Relations ...eiveceens csrsesnes 12.4.3 Temperature-Pressure Relations ....e.e. Cieeassas 12.4.4 Nomenclature for Kinetics Equations ..eeeeesees. 12.5 MSRE Characteristics Used in Kinetics Analysis .i.ceeees. 12.6 Preliminary STUAIES veuivrerenssecarostssasenssssoscencans 12.6.1 Early Analysis of React1v1ty Incidents «vieivesns 12.6.2 Comparison of MURGATROYD and ZORCH Results ..... 12.7 Results of Reactivity Accident Analyses ci.eveeressanses 12.7.1 Uncontrolled Rod Withdrawal Accident .eveievevees 12.7.2 Cold-Slug Accldent cvieievenensersnsneesens coe 12.7.3 Filling Accident veereeerinnnennonnorsanns ceeees 12.7.4 Tuel Pump PoOWEr FAIlUIe vveveeveeressonacnnennsos 12.7.5 ConCluSIiOn teeeensesrseesetseassscascssnsacannes BIOLOGICAL SHIELDING 4t eeeeeeeocesnsscssnsassssosssscnnnensas 13,1 General ..e.ieeeessorsrssssssssesssssessessssonssoscaneses 13,2 Overhead Biological Shielding .veeecevereen.. Cetiereaenn 13.2.1 Geometry ..... ceee s Ceseseercses et ettt aannnea 13.2.2 Bource Strengths svvveiiitreeeessennnens tesaesaa 13.2.3 Estimated Dose Rates .veeieerreocorensosncsonnense 13.3 ZLateral Biological Shielding .veeetvroescsseasscsscansnss 13.3.1 Basic Shield Arrangement ...ee.es e rs et aaaaases 13.3.2 South Electrical Service ROOM ¢ieseesess Cesaense 13.3.3 Cooclant Cell and Fan HOUSE +sevesecarons teresenes 13.3.4 Source Strengths teeieeiisseeasescscenssasennsssns 13.3.5 Calculation Methods s.viecvceceennns ceseerasanenn 13.4 Conditions After Reactor Shutdown ..eveeeceseoss Ceceran 1305 SUMMATY teiveescecststecetntsensssnsnnensscess ceraesaeans 13.6 DNomenclature for Biological Shielding Calculations ..... 112 112 112 113 113 114 121 viii MISCELLANEOUS teerevsvenerans theetsertesatareenne vresesresanns 179 14,1 Radiation Heating of Core Materials ..ecvvvnen. crscannn . 179 14,2 Graphite Shrinkage .eeeeveveceenees ettt seeesatetaneses 183 14.3 Entrained Gas in Circulating Fuel ..... veserecrnernnaees 184 14.3.1 Introduction ...... Ceteiesereranens Cirereesaaes . 184 14.3.2 Injection and Behavior Of G85 veeveceesnnss P < 14.,3.3 Effects on Reactivity ...ovvvvnn teasaeseresncana 185 14.4 Choice of Polson Material ....... cerreasans Cesebeveanss . 189 14.4.1 BOTOR cveseaans Ceeeretsessenaanans Crrereesnanns 189 14.4.2 Gadolinium .seeevees Cerri sttt et e et ennns Ceeereans 190 14.5 Criticality in Drain and Storage Tanks ceeeeeses. cevesss 191 REFERENCES ............. a " 8 @ " 0 S & 8 B 2 8 0 e e 4 5 8 & 8 8 PP G T e a e " 8 s v 0 196 MSRE DESIGN AND OPERATTIONS REPORT PART III. NUCLEAR ANALYSIS P. N. Haubenreich J. R. Engel B. E. Prince H. C. Clailborne ABSTRACT Preliminary considerations of the effects of core size and fuel-to-moderator ratio on critical mass and fuel concen- tration led to the specification of a core about 4.5 £t in diameter by 5.5 £t high for the MSRE. The average fuel frac- tion was set at 0.225, as a compromlse between minimizing the critical mass and minimizing the reactivity effects of fuel- salt permeation of the bare graphite moderator. The nuclear characteristics of the reactor were examined for three combinations of fissile and fertile material (UF, and ThF,) in a molten carrier salt composed of lithium, be- ryllium, and zirconium fluorides. Fuel A contained Thly (~1 mole %) and highly (~93%) enriched uranium (~0.3 mole %); fuel B contained highly enriched uranium (~0.2 mole %) and no fertile material; and fuel C contained uranium at 35% enrich- ment (~0.8 mole %) and no thorium. The radial distribution of the thermal neutron flux 1s strongly influenced by the presence of three control-rod thimbles near the axis of the core, with the result that the radial thermal flux maximum occurs about & in. from the axis. The axial distribution is essentially sinus- oidel. The magnitude of the thermal flux depends on the choice of the fuel; the maximum varies from 5.6 X 1013 neutrons cm™? sec™ for fuel B (at 10 Mw thermal) to 3.3 x 10*3 for fuels A and C. Both the fuel and the moderator temperature coeffi- cients of reactivity are substantially negative, leading to prompt and delayed negative power coefficients. Reactivity coefficients were also calculated for changes in uranium con- centration, Xet3? concentration, and fuel-salt and graphite densities. Temperature distributions in the fuel and graphite in the reactor were calculated for the design power level. With the fuel inlet and outlet temperatures at 1175 and 1225°F, re- spectively, the fuel and graphite reactivity-weighted average temperatures are 1211 and 1255°F, respectively. Fuel permea- tion of 2% of the graphite volume would increase the graphite weighted average temperature by 7°F. The power coefficient of reactivity with the reactor outlet temperature held con- stant is —0.006 to —0.008% 8k/k per M. Circulation of the fuel at 1200 gpm reduces the ef- fective delayed neutron fraction from 0.0067 to 0.0036. Xenon poisconing is strongly dependent on the major com- peting mechanisms of stripping from the fuel in the pump bowl and transfer into the bare graphite. The equilibrium poisoning at 10 Mw is expected to be between —1.0 and —1.7% 8k/k. The fuel contains an inherent neutron source of over 10° n/sec due to O,n reactions in the salt. This meets all the safety requirements of a source, but an external source willl be increase the flux for convenient monitoring of the subcritical reactivity. The total worth of the three control rods ranges from 5.6 to 7.69 Sk/k, depending on the fuel salt composition. Shutdown margins at 1200°F are 3.5% 8k/k or more in all cases. One rod will be used as a regulating rod to control the flux level at low power and the core outlet temperature at high power. In general, the reactor is self-regulating with respect to changes in power demand because of the nega- tive temperature coefficients of reactivity. However, the de- gree of self regulation is poorer at lower powers because of the low power density and high heat capacity of the system. The control rods are used to improve the power regulation as well as to compensate for reactivity transients due to xenon, samarium, power coefficient, and short-term burnup. Calculations were made for conceivable reactivity acci- dents involving uncontrolled control-rod withdrawal, "cold slugs,"” abnormal fuel additions, loss of graphite, abnormal filling of the reactor, and primary flow stoppage. No in- tolerable conditions are produced if the reactor safety system (rod drop &t 150% of design power) functions for two of the three control rods. The bioclogical shield, with the possible addition of stacked concrete blocks in some areas, reduces the calculated radiation dose rates to permissible levels in all accessible areas. 1. INTRODUCTION The design of the MSRE and the plans for its operation require information on critical fuel concentration, reactivity control, kinetics of the chain reaction, nuclear heat sources, radiation sources and levels, activation, and shielding. This part on Nuclear Analysis deals with these topics. Its purpose is to describe fully the nuclear char- acteristics of the final design of the MSRE and, to some extent, to show the basis for choosing this design. Methods and data used in the calcu- lations are described briefly. Detailed descriptions of the calculations and the sources of the basic data can be found in reports which are cited. 2. PRELIMINARY STUDIES OF CORE PARAMETERS 2.1 Introduction The original concept of the MSRE core was a cylindrical vessel con- taining 2 graphite moderator with small channels through which circulated a molten-salt fuel. During the early stages of MSRE deslgn, the nuclear effects of two importart core parameters were surveyed. These were the overall dimensions of the core and the ratio of fuel to graphite in the core. Most of the calculations were for one-regicn cores, but some cal- culations were made for cores consisting of two or three concentric re- gions of differing volume fractions. Critical concentration and inventory of U??° and the important coefficients of reactivity were the bases for comparison and for choice of the final design parameters. Some calculations were made for an alternative core design in which the fuel circulated through INOR-8 tubes in a graphite core. The nuclear characteristics of the reactor were calculated for several combinations of tube diameter and thicxness. A11 of these computations were performed on the IBM 704, using GNU, a multigroup, diffusion theory code.! Data from BNL-325 (ref 2) were used in preparing 34-group cross sections for the computations.3 The cross sections were averaged over & l/E spectrum within each group. Those used for thorium and U?38 in the resonance energy ranges were appropriate for infinite dilution in a moderator, and a temperature of 1200°F was assumed in determining the cross sections for the thermsl and last epi- thermal groups. In all of the calculations except some of those for tubed cores, the core materials were assumed to be homogeneously mixed within a region. 2.2 Effect of Core Size* The effect of core size was explored for cores containing 8 vol % fuel salt having the density and the nominal composition listed for fuel I in Table 2.1. Atomic densities of the constituents other than uranium were computed from this specificaticon, and the GNU code was used to compute the critical concentration of uranium. A graphite density of 1.90 g/cc was assumed. Table 2.1. Nominal Fuel Compositions and Densities Used in MSRE Survey Calculations Fuel type I II 11T Composition (mole %) LiF® 64 64 70 BeF, 31 31 23 ThF,, 4 0 1 Zr¥, 0 4 5 UF,° 1 1 Density (g/cc) 2.2 2.2 247 %0.003% 116, 99.997% Li”7. 93,56 U235, 6.5% U238, Computations were made for cores 5.5 and 10 ft high and 3.5, 4.0, 4.5, and 5,0 £t in diameter. Figure 2.1 shows critical concentrations of uranium obtained by these calculations. Also shown in Fig. 2.1 are U235 values of critical mass. These are the masses of in a core of the nominal dimensions. (A zero extrapolation distance was assumed.) 2.3 Effect of Volume Fraction in One-Region Cores 2.3.1 First Study” The first survey of the effect of varying volume fraction in a one- region core was for a core 4.5 £t in diameter and 5.5 £t high. Five different fuel volume fractions, ranging from 0.08 to 0.16, were con- sidered. The critical concentrations of uranium were computed, and these were used with the fuel volume fraction and the nominal core dimensions Ue33, U235 were also to compute critical masses of Total inventories of computed, assuming that an additional 46 ft3 of fuel is required outside the core. One set of calculations was made with fuel I of Table 2.1. In these calculations the graphite density was assumed to be 1.90 g/cc. Results are shown in Fig. 2.2 by the curves labeled "Composition A." UNCLASSIFIED ORNL— LR—DWG 50592A = = 3 16p] W < = 1 < O = = > & —_ Q 1 © © £ = 5 = & - 0 0 35 4.0 4.5 50 CORE DIAMETER (ft) Fig. 2.1. Critical Concentration and Mass as a Function of Core Size, A similar set of calculations was made with fuel II of Table 2.1, with the results shown in Fig. 2.2 by the curves labeled "Composition B." Not all of the differences in the two sets of curves are attributable to the substitution of zirconium for the thorium in the fuel salt, because a different graphite density, 1.96 g/cc, was used in the calculations for fuel IT, which would reduce critical concentrations for this case. UNCLASSIFIED ORNL—-LR-DWG 52050 80 160 ® INVENTORY, COMPOSITION A —-_ 70 ’///, 140 @ A / /‘ 120 €0 .\ — RN I ™~ INVENTORY, COMPOSITION B A —_ —f—————— \ g A & = = o 40 80 — M n 3 ' 3 D ® o CRITICAL MASS, COMPOSITION A | | 30 | — 60 —————— 20 ‘// ‘ 40 o/ CRITICAL MASS, COMPOSITION B —————— 10 A 20 0.08 0.10 0.12 0.44 0.16 VOLUME FRACTION FUEL SALT Fig. 2.2. Critical Mass and Total Inventory of U%3° as Functions of Fuel Volume Fraction, Calculated for Early Fuels. 2.3.2 Second Study5'6 After mechanical design and chemistry studies had led to firmer velues for the core vessel dimensions and the fuel composition, another study was made of the effect of fuel volume fraction, the results to be used in specifying the fuel channel dimensions. Core dimensions were 27.7-in. radius and 63-in. height, with extrapolation distances of 1 in. on the radius and 3.5 in. on each end added for the criticality calcula- tions. Fuel III of Table 2.1 was used, and a graphite density of 1.90 g/cc was assumed. Fuel volume fractions from 0.08 to 0.28 were considered. Calculated critical concentrations of uranium are shown in Fig. 2.3. Also shown are inventories of U??°, based on a fuel volume of 38.4 £t2 UNCLASSIFIED ORNL~ LR— DWG 57685 70 l CIRCULATING SYSTEM INVENTORY (kg OF U239) ~ & [ ] # \0-_._'___.. (;é} 20 - —e—0.2 2 = < o ; - 10+ — e - — 0.1 0 0 O 5 10 15 20 25 20 FUEL SALT (vol %) Fig. 2.3. Effect of Fuel Volume Fraction on Crit- ical Concentration and Inventory. v external to the core. The GNU results were also used to compute the re- activity changes resulting from fuel temperature changes and from the permeation of 7% of the graphite volume by fuel salt.* Results are sum- marized in Table 2.2. 2.4 Two- and Three-Region Cores’:® 2.4.1 Channeled Graphite Cores One way of reducing the critical mass is to use a nonuniform dis- tribution of fuel in the core, with the fuel more concentrated near the *This fraction was at that time the estimated fraction of the graphite volume accessible to kerosene. Table 2.2. Effect of Fuel Volume Fraction on Nuclear Characteristics of MSRE2 Fuel fraction (vol %) 12 14 16 20 24 28 Critical fuel conc. 0.296 0.273 0.257 0.238 0.233 0.236 (mole % U) Critigal mass (kg of 11.0 11.8 12.7 14.8 17.4 20.5 U23 ) SystemP U?35 51.0 48.6 47 ol 47.1 48 .7 524 inventory {(kg) Fuel temp. coeff. x 10° =3,93 —3.83 -3.70 =3.44 -=3.,16 —2.86 [(8k/k)/°F] Permeation effectC 11.4 9.7 8.3 6ol b o 3.5 (% &k/k) ®Core dimensions: 27.7-in. radius, 63-in. height, Nominal composition of fuel: LiF-BeF,-ZrF,-ThF,-UF,;, 70-23-5-1-1 mole %, Temperature: 1200°F, Fuel density: 2.47 g/cc, Graphite density: 1.90 g/cc. bCore plus 38.4 £t? of fuel. “Permeation by fuel salt of 7% of graphite volume. 10 center. This could be done in the MSRE by designing the graphite pieces to give a greater fuel volume fraction toward the center of the core. A reduction in critical mass, if accompanied by an increase in the concen- tration of U?2° in the fuel salt, does not necessarily imply a reduction in fissile material inventory in the MSRE because most of the fuel is external to the core. In order to explore the effects of nonuniform fuel distribution in the MSRE, a set of calculations was made in which the core was subdivided into either two or three regions with different fuel volume fractions. Fuel IIT of Table 2.1 and graphite having a density of 1.90 g/cc were assumed. Overall dimensions of the core were taken to be 27.7-in. radius and 63-in. height. Radial and axial extrapolation distances of 1 and 3.5 in. were added to these dimensions. The critical fuel concentration, the core inventory (or critical mass), and the total inventory were computed. Flux and power distributions were also obtained. Three cases of two-region cores were considered. In each the core consisted of two concentric cylindrical regions, with the inner con- taining 24 vol % fuel and the outer, 18 vol % fuel. Results are sum- marized in Table 2.3. Table 2.3. Some Characteristics of Two-Region Reactors critical fuel o itical Mass System® Inventory Volume Ratio® C trati ciume h&atlo ?Irlll(olig ?rf;aU;on (kg of U235) (kg of U235) 50/50 0.232 15.1 46,5 60/40 0.234 15.7 47 oo 70/30 0.236 16.3 48 o4 ®Ratio of inner region (24 vol % fuel) to outer region (18 vol % fuel). bIncluding 38.4 £t external to the core. 11 In the three-region cases the core was divided into concentric regions of equal volume. Thirteen cases were calculated, with the re- sults shown in Table 2.4, Although the critical mass was markedly re- duced in some cases, this was accompanied by a higher fuel concentration, which raised the fissile material inventory external to the core. As a result, in no case was the total inventory greatly reduced below the minimum for one-region cores. The heat generation per unit volume of fuel follows closely the shape of the thermal neutron flux in all cases. Table 2.4 shows that the ratio of radial peak to average thermal neutron flux was significantly reduced in some cases. (For a uniform core the ratio is 2.32.) The ef- fect on flux shape is illustrated for some of the cases in Fig. 2.4. Table 2.4. Some Characteristics of Three-Region Reactors Fuel Critical Fuel Critical Sy stem® Thermal Flux Fraction® Concentration Mass Inventory Ratioc, Radial (vol %) (mole % U) (kg of U?3°) (kg of U?3?) Peak/Av 25, 13, 7 0.243 11.3 4 a2 1.86 40, 13, 7 0.273 16.9 53.8 1.45 10, 13, 7 0.324 10.1 54,0 2.38 25, 20, 7 0.237 12.8 45.1. 2.03 25, 6, 7 0.257 10.1 44 9 1.69 25, 13, 10 0.243 12.0 4 8 1.89 25, 13, 4 0.243 10.5 43.3 1.84 40, 20, 7 0.272 18.8 55.6 1.48 10, 6, 7 0.361 8.6 57.5 2.18 25, 20, 10 0.237 13.5 45.7 2.06 25, 6, 4 0.258 9.3 b y2 1.66 40, 13, 10 0.273 17.8 54.8 1.45 10, 13, 4 0.325 9.1 53.0 2.35 a . . . . In inner, middle, and outer concentric regions of equal volume. bIncluding 38.4 ft° external to the core. 12 UNCLASSIFIED ORNL—LR— DWG 55954A 2.5 T . - | | ‘\\\\Q UNIFORM 1.5 (0.25. 0.13, 0.07) P L _{0.40, 0.13,0.07) — i {0.40, 0.13, 0.07) 1.0 ! N \ (0.25,0.13, 0.07) 0.5 j UNIFORM ::\\ (0.10, 0.13, 0.07) { 1 (THERMAL FLUX)/{MEAN THERMAL FLUX) o | 0 5 10 t5 20 25 30 35 SPACE POINT NUMBER Fig. 2.4. Comparison of Thermal Flux Shapes in Three-Region Reactors. Numbers in parentheses refer to fuel volume fraction in inner, middle, and outer region of reactor, respectively. Table 2.5. Characteristics of Cores with Lumped Moderator Critical Concentration Critical Mass Moderator (mole % ) (kg of U235) 5-in. Reflector Thickness, No Island Graphite 1.04 250 Be 0.72 175 BeO 0.76 186 10-in. Reflector Thickness, l-ft-dlam Island Graphite 0.67 93 Be 0.25 34 BeO 0.28 39 2.4.2 Cores with Moderator in Reflector and Island® Brief consideration was given to a core which was essentially one large fuel channel, with the moderator confined to a surrounding region i3 and a central island. Calculations for this type of core were made as an adJjunct to those for the multiregion, channeled graphite cores, using the same fuel and overall core dimensions. Three moderators were con- sidered: graphite (p = 1.90 g/ce), beryllium (p = 1.84 g/cc), and be- ryllium oxide (p = 2.90 g/cc). Typical results are given in Table 2.5. 2.5 Cores Containing INOE~8 Tubes Nuclear characteristics were also computed for cores in which the fuel was contained in tubes of INOR-8 passing through the core. The preliminary calculations for this type of core treated the fuel, graphite, and INOR-8 of the core as a homogeneous mixture. Results of these calcu- lations were reported in MSRP progress reports.®»” In later calculations, hitherto unreported, the GNU code was used to calculate flux distributions and disadvantage factors in a typical cell of fuel, INOR-8, and graphite. When the heterogeneity of the core was taken into account, calculated critical concentrations were increased over those from the homogeneous approximation. Results of the heterogeneous calculations are given in Table 2.6. 2.6 Conclusions At a very early stage of the design it was decided that the core would be approximately 4.5 £t in diameter and 5.5 £t high after some calculations showed that the critical mass was relatively insensitive to core dimensions around this point (Fig. 2.1). The volume fraction of fuel in the core was set at 0.225 after cal- culations showed that a fraction of 0.24 gave the lowest critical concen- tration of uranium and that the reactivity increase due to fuel perme~ ation of the graphite was much lower around this point than at lower volume fractions. (Four half-channels O0.2- by l.2-in. in each 2- by 2-in. graphite block were chosen to give a fuel fraction of 0.24; round- ing the corners of the channels reduced the fraction to 0.225.) Only brief consideration was given to cores of two or three regions with differing volume fractions, because calculations showed these had little, if any, advantage over the uniform, one-region core. Table 2.6. Some Characteristics of Cores with INOR-8 Tubes Fuel fraction (vol %) 10 10 10 14 14 14 18 18 18 Tube thickness (mil) 40 60 80 40 60 80 40 60 80 Critical fuel conc. 0.74 0.96 1.22 0.64 0.86 1.12 0.62 0.86 1.15 (mole % U) system U?3° inventory (kg) 128 165 210 118 158 206 122 169 226 Neutron Balance Absorptions: INOR g.7 10.9 12,5 10.7 12.3 13.8 10.6 12.8 l4.1 graphite + salt 2.9 2.5 2.1 2.5 2.0 1.7 2.2 1.7 1.4 Ue3° 50 .4 50.9 51.3 50.9 51.5 52.2 51.5 52.3 53.3 y238 0.4 0.5 0.6 0.5 0.6 0.7 0.6 0.8 0.9 Th 3.0 2.7 2.5 4al 3.7 3.3 5.0 beals 4.0 Fast leakage 24,9 2445 24.1 24 o4 24,5 2440 25.1 2b o4 23.6 Slow leakage 9.7 8.0 6.9 6.9 5et 4.3 5.0 3.6 27 Note: Core radius, 27.7 in.; core height, 63 in.; fuel volume external to core, 40 ft2; nominal fuel composition, LiF-BeFp-ZrF,-Tht,-UF,, 70-23-5-1-1 mole %; tube OD, 3 in. T 15 3. CRITICALITY, FLUX DISTRIBUTIONS, AND REACTIVITY COEFFICIENTS 3.1 Description of Core The final design of the core and reactor vessel is ghown in the cut- away view in Fig. 3.1. Fuel salt, after entering through a flow distrib- utor, passes down through an annular region between the INOR-8 vessel and the INOR-8 core can to the lower head. The lower head contains anti-swirl vanes which direct the flow inward and a moderator support grid, both of INOR-8, The fuel flows from the lower head up through a iattice of hori- zontal graphite sticks, through the channeled region of the core and into the upper head. The channeled region of the core consists of 2-in.-square, vertical graphite stringers, with half-channels machined in each face to provide fuel passages. The regular pattern is broken near the axis of the core, where three control rod thimbles and a graphite sample assembly are located. TFigure 3.2 shows a typical fuel channel and the section around the core axis. 3.2 Calculational Model of Core Critical fuel concentrations, flux and power distributions, and re- activity coefficilents were calculated for the reactor, taking into account as much detaill as was practical, The actual core configuration was rep- resented for the nuclear calculations by a two-dimensional, 20-region model in r-z geometry (cylindrical with angular symmetry). This model is shown in vertical section in Fig. 3.3, indicating the relative sizes and positions of the regions within which the material composition was con- sidered to be uniform. The region boundaries and the volume fractions of fuel, graphite, and INOR-8 in each region are summarized in Table 3.1, The boundaries of each of these 'macroscopic" regions were chosen to rep- resent as closely as possible those gross geometrical and material prop- erties which determine the neutron transport in the core. This choice was made within the practical limitations on the number of dimensions and mesh points in the numerical calculations. Use of two-dimensional geometry resulted in a large saving in com- puting time, and was considered an adequate representation for most pur- poses. The major approximation involved wasg in the representation of the UNCLASSIFIED ORNL-LR-DWG 61097R FLEXIBLE CONDUIT TO CONTROL ROD DRIVES SAMPLE ACCESS POR COOLING AIR LINES ACCESS PORT COOLING JACKETS FUEL OUTLET REACTOR ACCESS PORT CONTROL ROD THIMBLES CORE //f//// CENTERING GRID FLOW DISTRIBUTOR GRAPHITE-MODERATOR) STRINGER \ FUELINLETJ/ REACTOR CORE CAN— - REACTOR VESSEL—T: *’fiz;ERATOR SUPPORT GRID ANTI-SWIRL VANES VESSEL DRAIN LINE Fig. 3.1. Cutaway Drawing of MSRE Core and Core Vessel. 17 UNCLASSIFIED REACTOR § ORNL-LR-DWG 60845A1 CONTROL ROD \\-\-- GUIDE TUBE 31— GUIDE BAR TYPICAL — FUEL CHANNEL §§§§ - R -~ R - R - REACTOR ¢ ~=— 2,00 *! /) ' R 7N\ 0.200-in. R~ g N~ 0.400 1.~ R = REMOVABLE STRINGER 4 GRAPHITE IRRADIATION ¢ SAMPLES ( 7/g-in.DIA) ~ | 2 in. TYPICAL Y Fig. 3.2. MSRE Control Rod Arrangement and Typi- cal Fuel Channel. small central region of the core which includes the three control rod thimbles and the graphite specimens. The model contains the same amounts of fuel, graphite, and INOR-8 as the actual core, but the arrangement is necegsarily different. The INOR-8 is of the thimbles represented by a C,e10~in, ~thick, 6.00-in.-0D annulus, which has a volume and an outside surface area equal to those of the INOR-8 of the three thimbles. Just inside the INOR-8§ annulus is a region containing low-density fuel, repre- senting a mixture of the voids inside the thimbles and the extra fuel sur- rounding the thimbles and the specimens, At the center of the core is a cylinder of normal core composition (0,255 fuel, 0.775 graphite by volume). Other assumptions made in the calculations are that the temperature is uniform at 1200°F, that there is no permeation of the graphite by the fuel, and that there are no fission product poisons in the core. The graphite was assumed to be pure carbon, with a density of 1.86 g/cc. Re- activity effects due to deviations from these assumptions were tested asg perturbations, as described later in this chapter. .18: UNCLASSIFIED ORNL~LR-DWG 73610R - i o|2 C Lel o b ol 1.1 02 46 8 10 ' INCHES - Fig. 3.3, Twenty-Region Core Model for Nuclear Calculations. Table 3.1 for explanation of letters. 4) W See Table 3.1. Twenty-Region Model of MERE Core Used in Nuclear Calculations (See Fig. 3.3 for graphical location of regions) Radius (in.) Height (in.) Composition (vol %) Region Region Represented Inner Outer Bottom Top Fuel Graphite INOR-8 A 0 29.56 74,92 76 .04 0 0 100 Vessel top B 29.00 29,56 -92.14 74,92 0 100 Vessel side C 0 29.56 —10.26 -9.14 0 0 100 Vessel bottom D 3.00 29.00 6747 74.92 100 0 0 Upper head BE 3.00 28.00 66.22 67.47 93.7 3.5 2.8 F 28.00 29.00 0 67.47 100 0 0 Downcomer G 3.00 28.00 65.53 66,22 4.6 5.4 0 H 3.00 27475 64459 65.53 63.3 36.5 0,2 I 27.75 28.00 0 65.53 0 0 100 Core can J 3,00 27.75 5.50 64.59 22.5 77.5 0 Core K 2,90 3.00 5.50 74.92 0 0 100 Simulated thimbles L 0 1.94 2.00 64459 22.5 77.5 0 Central region M 1.94 27,75 2.00 5.50 2245 77.5 0 Core N 0 27.75 0 2.00 23.7 76.3 0 Horizontal stringers 0 0 22.00 —l.41 0 66.9 15.3 17.8 P 0 29.00 -9.14 -1.41 90,8 0 9.2 Bottom head Q 0 1.94 66,22 74.92 100 0 0 R 0 1.94 65.53 66,22 g9.9 10.1 0 S 0 1.94 64.59 65.53 43.8 56,2 0 T 1.94 2.90 5.50 74,92 1008 0 0 Fuel and voids aDensity, 0.46 X density of normal fuel. 61 20 3.3 Fuel Properties The nuclear characteristics of the reactor were calculated for three different fuel salts, deseribed in Table 3.2. (Uranium concentrations are approximate, based on Initial estimates of concentrations required for criticality. The exact critical concentrations are given in Sec 3.9.) 3.4 Cross Sections and Effects of Inhomogeneity of Core The group cross sections to be used in diffusion calculations prop- erly should take into account the effect of fuel composition and lumping on the neutron energy spectra and spatial distributions in the fuel and in the graphite. Table 3.2, MSRE Fuel Salts for Which Detailed Nuclear Calculations Were Made Fuel Type A B C Salt composition (mole %) LiF> 70 66.8 65 BeFs 23,7 29 29,2 ZrF, 5 e 5 ThF, 1 0 0 UF,; (epprox) 0.3 0.2 0.8 Uranium composition (atom %) U234 1 1 0.3 U23° 93 93 35 U236 1 1 0.3 U238 5 5 YA Density at 1200°F (1b/ft3) 144.5 134.5 142.7 999,9926% 117, 0.0074% LiS. 21 3.4.1 Resonance Neutrons Fuels A and C contain important amounts of strong resonance absorbers, thorium in fuel A and U?2% in fuel C., The effective resonance integrals for these materials depend on their concentration in the fuel and on the effective surface-to-volume ratio of the fuel channels. Figure 3.4 1lius- trates how the effective resonance integral Tfor U238 varies over the con- centration range of interest for the MSRE., This curve was calculated by Nordheim's numerical integration program for resonance integral computa- tions.® In this calculation, the actual two-dimensional transverse sec- tion of the MSRE lattice geometry (Fig. 3.2) was approximated by slab geometry with a surface-to-volume ratio of salt equal to the effective UNCLASSIFIED ORNL DWG, 63-3147 260 240 B= 220 200 180 1?38 EFFECTIVE RESONANCE INTEGRAL (barns) 160 1ko 0 0.2 0.4 0.6 0.8 1.0 238 U™"F, CONCENTRATION (Mole %) Fig. 3.4. Variation of U?2® Effective Resonance Integral with U?38F, Concentration in MSRE Lattice. 22 ratio in the actual lattice. The effective ratio is affected by Dancoff effects (shielding from neighboring channels), which reduces the effective surface-to-volume ratio for resonance capture in the MSRE lattice by about 30%.9 These calculations of effective resonance integrals were used in initial estimetes of the critical concentration of U??° in each fuel. In preparation for the refined calculations of critical concentra- tion, which were to be done by a 33-group diffusion method, a new set of multigroup cross sections was prepared for the core with each of the three fuel compositions. Group cross sections for the 32 fast groups were gen- erated by use of the IBM 7090 program GAM-1,10 This program is based on a consistent P-1 approximation to the Boltzmann equation for neutron slow- ing-down, and averages the cross sections over an energy spectrum above thermal which is appropriate for a single-region reactor with a macro- scopically uniform composition. Corrections for the shielding effects associated with the fuel channels are automatically included in the GAM-1 program. For the MSRE calculations, a set of cross sections was generated for each fuel composition, assuming a one-region reactor with a lattice like that in the main part of the actual core (22,5 vol % fuel, 77.5 vol % graphite). A minor complication in the GAM-1 calculation of MSRE cross sections was that the available version of the GAM-1 cross-section library tape did not include Lis, Li7, and Flg, which are important components of the MSRE fuel. This was circumvented by simulating their effect on the neutron spectrum by the inclusion of an amount of oxygen equivalent in slowiling- down power (gzs) to the lithium and fluorine actually present. Fast group cross sections for Li6, Li7, and F'? were compiled from basic cross-sec- tion data, independently of the GAM-1 calculation. 3¢4.2 Thermal Neutrons Average cross sections for the thermal group were calculated by use of two thermalization programs for the IBM 7090. Reference calculations for each fuel at 1200°F were made with THERMOS, which computes the thermal spectrum in a one-dimensional lattice cell.l! The cell model used was that of a cylindrical graphite stringer, surrounded by an annulus of salt. For other calculations in which the effects of changes in temperature and 23 thermal cutoff energy were studied, a simpler and more rapid thermaliza- tion program was employed, based on the Wilkins "heavy gas" space-inde- prendent model. Lumping reduces the thermal utilization in the MSRE lattice because of the thermal flux depression in the fuel, but this effect is not large. (For salt with the maximum uranium content of interest in the MSRE, 1 mole % UF;, the flux depression in the fuel was about 3.5%.) Furthermore, the normal temperature of 1200°F is above the temperature at which crystal binding effects in graphite must be considered.l® TFor these reasons, it was found that good agreement with the THERMOS model could be obtained by combining the Wilkins thermal spectrum calculation with a one-group P-3 calculation of the spatiasl disadvantage factor. These approximations were used wherever possible in order to save computer time. For some of the studies of the temperature coefficient of reactivity, however, it was necessary to use the THERMOS program in order to vary the temperature of the fuel channel independently of that of the graphite. These studies are described more fully in Sec 3.7. 3.5 Criticality Calculations Critical fuel concentrations were computed with MODRIC, a multigroup diffusion program for the IBM 7090, MODRIC is a one-dimensional program with provision for approximating the neutron leakage in the direction transverse to that represented in the one-dimensional model. For the calculation of critical concentration, the reactor was represented by a cylinder with regions and materials corresponding to the midplane of the model shown in Fig. 3.3, Axial leakage was taken into account by the in- clusion of a specified axial buckling, based on earlier calculations of the axial flux shape. In the computations for fuels A and B, the concen- trations of all uranium isotopes were varied together in all regions to find the critical concentration. For fuel C, the U?38 concentration was held constant and those of the other uranium isotopes were varied. (Re- sults are summarized in Table 3.5, Sec 3.9,) 24 In addition to the critical concentration, the MODRIC calculations gave two-group constants for each region represented. These were to be used in & two-group, two-dimensional calculation. It was therefore nec- egssary to perform other MODRIC calculations to include regions missed by the midplane radial calculations. For these calculations the reactor was represented by a multilayer slab, with regions corresponding to an axial traverse through the model of Fig. 3.3, and a radial buckling based on the radial MODRIC calculations, ©Slabs corresponding to two different traverses were calculated, one corresponding to the core centerline and the other to a traverse just outside the rod thimbles. These axial cal- culations, using the critical concentrations given by the radial calcula- tions, gave values of keff between 1,004 and 1.021. This is considered to be good agreement, in view of the fact that the axial calculations are less accurate than the radial because the equivalent transverse buckling is more subject to error in the axial calculations,. The two-group constants obtained from MODRIC were used in calcula- tion of the model of Fig. 3.3 by the two-group, two-dimensional program EQUIPOISE-3.1% 19 These two-group calculations gave keff of 0.993, 0.997, and 0,993 for fuels A, B, and C, respectively, further confirming the critical concentrations found by the radial MODRIC criticality search. In all of these calculations it was assumed that the core tempera- ture was uniform at 1200°F, the control rods were withdrawn, and the core contained no fission product polsons. The calculated critical concentra- tions are therefore those which would be attained during the initial crit- ical experiments with clean, noncirculating fuel and with all rods fully withdrawn. During subsequent operations, the concentration must be higher to compensate for all of the effects (poisons, rods, and the loss of de- layed neutrons) which tend to decrease reactivity. The total of these effects is expected to be about 4% dk/k. Table 3.5 (Sec 3.9) lists the critical concentration for normal operation, which would include these effects, The increases in the critical concentration from the clean crit- ical experiment were computed from values of the concentration coefficient of reactivity (3k/k)/(8C/C), produced by the MODRIC criticality searches. 25 3,6 TFMux and Fission Distributions 3.6.1 Spatial Distribution Two-group fluxes and adjoint fluxes were produced by the EQUIPOISE-3 calculations. TFigures 3.5-3.8 show the axial and radial distributions Tor fuels B and C. The fluxes for fuel A are within 2.,5% of those for fuel C. The radial distributions are for an axial position that corre- sponds to the maximum in the thermal flux, which is at a position very close to the core midplane., The axial distributions are at a position 8.4 in. from the core centerline*; this radius corresponds to the maximum value of the thermal flux. The MODRIC calculations gave gpatial flux distributions for each of 33 energy groups. 1t was necessary to normalize the MODRIC fluxes to cor- respond to the neutron production at 10 Mw, and the normalization factor was obtained by comparing the MODRIC thermal fluxes with the 10-Mw values computed by EQUIPOISE. (The shapes of the thermal fluxes were very sim- ilar.) The high-energy MODRIC fluxes were then multiplied by the normal- ization factor to obtain the predicted high-energy neutron fluxes in the reactor., Figure 3.9 shows the radial distribution, near the core mid- plane, of the neutron fluxes with energies greater than 0.18 Mev and with energies greater than 1.05 Mev., Figure 3.10 shows the axial distribution of the same energy groups 3 in. from the core centerline, which is about the location of the rod thimbles and the test specimens. (The values shown in Figs. 3.9 and 3.10 were computed for fuel C, but these wvery-high- energy fluxes are not sensitive to the fuel composition.) The spatial distributions of the fission density were obtalned from the EQUIPOISE-3 calculations. Figures 3.11 and 3.12 show the axial and radial distributions of the fission density in the fuel, for fuel C. The same calculations also gave total fissions in each region., Table 3.3 sum- marizes, for fuel C, the fraction of the total fissions which occur in the major regions of the reactor. *The datum plane for the axial distance is the bottom of the hori- zontal graphite bars at the bottom of the core. UNCLASSIFIED ORNL DWG. 63.8148 . c TS SUod 20 -~ s 80 70 30 40 AXIAL POSITION (in.) 20 10 -10 from Core 11. 8.4 Axial Distribution of Two-Group Fluxes Fig. 3.5. Center Line, Fuel B. (x 1073) (x 10%9) ) -1 sec -2 FAST FILUX (neutrons cm -10 0 10 20 30 Lo 50 60 AXTAL POSITION (in.) Fig. 3.6. Axial Distribution of Two-Group Fluxes 8.4 in. Center Line, Fuel C. UNCLASSIFIED ORNL DWG, 63-8149 z ppy Slhean 70 80 from Core L 28 1 UNCLASSIFIED (x 10 3) ORNL DWG. 638150 ****** 1 ) 5 sec” -2 FLUX (neutrons cm ........ ...... +++++ 0 5 10 15 20 25 30 RADIUS (in.) Fig. 3.7. Radial Distribution of Two-Group Fluxes Near Core Mid- plane, Fuel B. 29 (x 1013) UNCLASSIFIED ORNL DWG, 638151 16 14 12 ~ T r-;] 4] o 10 @ @ @ o o g 1 u & o w o g a o 8 2 B g 3 a O ~ . 5 & E — g © % 2 P & L 2 0 SAEE Shethon : 0 5 10 15 20 25 30 RADIUS (in.) Fig. 3.8. Radial Distribution of Two-Group Fluxes Near Core Mid- plane, Fuel C. 30 (x 1013) UNCLASSIFIED ORNL DWG. 63.8152 -2 sec FLUX (neutrons cm 0 5 10 15 20 25 30 RADIUS (in.) Fig. 3.9, High-Energy Neutron Fluxes: Radial Distribution Near Core Midplane at 10 Mw. sSec FIUX (neutrons cm = ol -10 0 Fig, 3,10, 10 UNCLASSIFIED ORNL. DWG, 63.8153 ¢¢¢¢¢¢ 20 30 ] 50 60 70 AXTAL POSITION (in.) High-Energy Neutron Fluxes: Axial Distribution 3 in. from Core Center Line at 10 Mw. TE UNCLASSIFIED ORNL DWG. 63.8154 REIATIVE FISSION DENSITY, 0 5 10 15 20 25 30 RADIUS (in.) Fig. 3.11. Radial Distribution of Fuel Fission Density Near Core Midplane, Fuel C. REIATIVE FISSION DENSITY UNCLASSIFIED ORNL DWG. 63-.8155 1.0 T : ; 0.8 o 0.6 0.4 -10 0 10 20 30 4O 50 £0 70 8o 7, AXIAL POSITION (in.)} Fig. 3.12. Axial Distribution of Fuel Fission Density 8.4 in. from Core Center Line, Fuel C. 23 34 Table 3.3, Fission Distribution by Major Region (See Fig. 3.3 for graphical location of regions) Fraction of Total Fissions Major Region Regions (4) Downconmer T 2.9 Lower head o, P 2ot Main core J, L, M, N, T 89.1 Upper head D, E, G, H, Q, R, S 5.6 3.6.2 Energy Distribution The energy distribution of the neutron flux at a given location is influenced by the nuclear properties of the materials in the general vi- cinity of the point. As a result, the flux spectrum varies rather widely with position and fuel composition. The MODRIC calculations produced av- erage distributions of flux as a function of energy within each reactor region as well as the detailed distributions as functions of position and energy. Figure 3,13 shows the average fluxes, per unit lethargy, in the largest core region (Region J of Fig. 3.3) for each of the 32 nonthermal energy groups. The fluxes are normalized to unit thermal flux in each case. The maximum lethargy of the thirty-second or last epithermal group is 17, which corresponds to a neutron energy of 0.414 ev. This is also the maximum energy (minimum lethargy) of neutrons in the thirty-third or "thermal" group. The effect of the strong resonance absorbers, thorium in fuel A and U%3® in fuel C, in reducing the flux in the region just above the thermal cutoff is readily apparent. The distribution of fissions as a function of the lethargy of the neutrons causing fission is the product of the neutron flux and the fis- sion cross section, Figure 3.14 shows the average fission density, per unit lethargy, in the largest core region, normalized to one fission in that region, as a function of neutron energy for fuel C. The resonances in the fission cross section are reflected by the peaks at the higher lethargies (lower energies). Integration of the plot in Fig. 3.14 to a NEUTRON ENERGY (ev) UNCLASS!FIED ORN{L. DWG., 63.81556 107 10° 10° 1% 103 10° 10 1 0.35% 0.30 0.25 o O 0.20 = 2 1& 0.15 0.10 0.05 0 4 6 8 10 12 1k 16 18 LETHARGY, u Fig. 3.13. Average Flux Spectra in Largest Core Region. Ge UNCLASSIFIED ORNL DWG. 63.8157 NEUTRON ENERGY (ev) 1 10 LETHARGY, u Density as a Function of Lethargy of Neutrons ission Fig. 3.14. F Causing Fission, Fuel C. 106 w (e (W)= /1™ (0)73) o 37 given lethargy gives the cumulative fraction of fissions caused by neu- trons with less than the specified lethargy. Figure 3.15 illustrates the result of this operation for fuel C in the largest core region. This figure indicates that 17.7% of the fissions in this region are caused by nonthermal neutrons, The average fraction for the entire reactor is 20.2%, indicating that fast fissions account for a relatively larger fraction of the total in other regions. This 1s particularly true in the upper and lower heads, where the absence of graphite produces a much lower ratio of thermal to fast flux than exists in the main portion of the core. 3.7 Reactivity Effects of Nonuniform Temperature Changes in the temperature of the core materials influence the re- activity through changes in the neutron leakage and absorption probabili- ties. The reactivity change between two isothermal conditions can be ex- pressed in terms of a single temperature coefficient of reactivity. When the reactor operates at power, however, the core is not isothermal; in fact, the overall shapes of the temperature distributions in the fuel and in the graphite are quite dissimilar. For this reason, and also because different thermal time constants are involved in fuel and graphite tem- perature changes, separate consideration of the reactivity effects of these changes 1s necessary. To delineate the factors governing the reac- tivity-temperature relation, calculations were first performed using a simplified model of the reactor, that of a single-region cylinder in which composition and temperature were macroscopically uniform. These are dis- cussed in Sec 3.7.1l. Analysis based on the multiregion model of Fig. 3.3 is considered in Sec 3.7.2. 3.7.1 One-Region Model For this analysis, use was made of the GAM-1 program in order to calculate macroscopic cross sections averaged over the energy spectrum above thermal. Cross sections for the thermal group were averaged over a Wilkins spectrum. The lower energy cutoff for the GAM-1 calculation was equal to the upper cutoff for the Wilkins thermal spectrum. The two- group parameters obtained in this way were then used to calculate the 38 UNCLASSIFIED ENERGY OF NEUTRON CAUSING FISSION (ev) UNCLassIFIED 107 108 10° ot 103 10° 10 1 0.20 0.10 CUMULATIVE FRACTION OF FISSICNS 0 2 4 6 8 10 12 14 16 18 LETHARGY OF NEUTRON CAUSING FISSION Fig. 3.15, Cumulative Fraction of Fissions Caused by High-Energy Neutrons, Fuel C. 39 multiplication constant of the cylinder, based on the standard two-group diffusion equations. In this calculation, the geometric buckling used was that of a cylinder, 59 in, in diameter by 78 in. high. Three tem- perature conditions were considered: (1) salt and graphite at 1200°F, (2) salt at 1600°F, graphite at 1200°F, and (3) salt and graphite at 1600°F. The temperature coefficient of reactivity was obtained from the approximate relation 1 3k x(2600) _ y(1200) EST = (3.1) 200 k(lQOO) Two special considerations are of importance in analysis of tThe MSRE temperature coefficlent. The first is the position chosen for the thermal energy cutoff, which 1s the approximalte energy above which thermal motion of moderator atoms may be neglected. Since a cylindrical core of this size has a large neutron leakage fraction, unless the cutoff energy is chosen high enough the total effect of temperature on thermal neutron leakage is underestimated. This effect is indicated in Fig. 3.16, curve (a). Here the total temperature coefficient of reactivity (fuel + graph- ite) of the core fueled with fuel C is plotted vs the upper energy cutoff of the thermal group. The coefficient tends to become independent of the cutoff energy for cutoffs in excess of about 1 ev. The second consideration is the effect of the salt temperature on the thermal spectrum. For this calculation, it was necessary to employ the THERMOS program so that the temperatures of the salt channels and graphite could be varied independently. The results of this analysis for fuel C may be seen by comparing curves (b) and (c¢) in Fig. 3,16. Curve (b) was calculated by neglecting the change in thermal spectrum with salt temperature. This difference is a consequence of the fact that the light elements in the salt, lithium, beryllium, and fluorine, contribute sub- stantially to the total moderation in the MSRE core. Similar calculations based on the one-region cylindrical model were made for fuels A and B. The values of the reactivity coefficients for all fuels obtained at the asymptotic cutoff energies are summarized in Table 3.4. All calculations were based on the wvalues of volumetric ex- pansion coefficients at 1200°F (see Table 3.4). 40 - UNCLASSIFIED (x 10 5) ORNL DWG. 68159 TEMPERATURE COEFFICTENT OF REACTIVITY [(°F) ] CUTOFF ENERGY (ev) CURVES: Included (a) Total (Fuel + Graphite) (b) Fuel; Thermal Spectrum Assumed Independent of Salt Temperature (c¢) Fuel; Dependence of Thermal Spectrum on Salt Temperature Fig. 3.16. Effect of Thermal Cutoff Energy on Temperature Coeffi- cient of Reactivity, Fuel C. Table 3.4. Temperature Coefficilents of Reactivity Obtained from One-Region Model (Calculations based on expansion coefficients, at 1200°F, of 1.18 X 1072 ¢/°F for salt and 1.0 X 1072 ¢/°F for graphite) Fuel A Fuel B Fuel C Temperature coefficient of reactivity [(8k/k)/°F] salt —3.03 X 1077 ~4,97 X 107 =3.28 x 1077 Graphite —3,36 X 1077 —=4.91 x 1072 -3,68 x 10°° Total —6.39 X 107° -9.88 x 1077 —6,96 x 1077 41 3.7.2 Multiregion Model To study the effects of the macroscopic distribution of materials composition and temperature on the reactivity-temperature relations, use was made of first-order perturbation theory.16 For this purpose, it 1is convenient to utilize the concept of a nuclear average temperature, This quantity is defined as follows: At low power, reactor criticality is assumed to be established at isothermal conditions in fuel and graphite. Then, with the graphite temperature held constant, the fuel temperature is varied according to a prescribed distribution, thus changing the re- activity. The fuel nuclear average temperature, T;, is defined as the equivalent uniform fuel temperature which gives the same reactivity change as that of the actual temperature distribution. Similarly, the graphite nueclear average temperature, Tg, is defined as the uniform graphite tem- perature which gives the same reactivity change as the actual graphite temperature profile, with the fuel temperature held constant. The relations between the nuclear average temperature, T*, and the temperature distributions, T(r,z), are of the form * j;eactOr Tx(r,z) GX(T,Z)r dr dz reactor Gx(r,z)r dr dz where * * % . and ¢1, %5, ¢:, ¢: are the unperturbed values of the fast and slow fluxes and the fast and slow adjoint fluxes, respectively., The coefficients Gij are constant over each region of the unperturbed reactor in which the nu- clear composition is uniform, but vary from region to region. These quan- tities involwve the temperature derivatives of the macroscopic nuclear constants; that is, in obtaining Eq. (3.3), the local change 3% in the macroscopic cross sections was related to the local temperature change OT through the approximation 8x(r,z) = g% I (r,z) . (3.4) 42 This approximation is adequate 1f the gpatial wvariation in temperature is relatively smooth within a given region. Temperature coefficients of reactivity which are consistent with the definitions of the nuclear average temperatures were also obtained from perturbation theory., The complete temperature-reactivity relation is ex- pressed as Bk ¥ ¥ * K - = 0BT, + agSTg , (3.5) where * * * 3T = T — Tg (3.6) * and & 1is the appropriate temperature coefficient of reactivity. The fuel and graphite reactivity coefficients are related to the weight func- tions G(r,z) as follows: ¢ (r,z)r dr dz . . , o = reactor x (3.7) X j;eactor F(r,z)r dr dz where * * F(I’,Z) = V2f1¢1¢1 + V2f2¢2¢2 . (3.8) The principal advantage ol expressing the reactivity change with tempera- ture in the form of Egq. (3.5) is that the reactivity coefficients, a*, and the weight functions G(r,z) depend only on the conditions in the un- perturbed reactor. Use of this approximation thus simplifies the calcu- lation of the reactivity effects of a large number of temperature distri- butions. Reactivity coefficients and temperature weight functions for the fuel salt and graphite were evaluated for the 20-region model of the MSRE core (Fig. 3.3), fueled with fuel C. The resulting weight functions are shown in Figs., 3.17-3.20. These figures correspond to axial and radial traverses of the core which intersect at the approximate position of max- imum thermal flux. Corresponding weight functions for fuels A and B do not differ qualitatively from these results. The discontinuities in the welght functions occur as the effective concentrations of salt, graphite, REIATIVE IMPORTANCE 1.0 Fig. 3.17. as a Function of Line, UNCLASSIFIED DWG. 63.8160 10 20 30 40 50 60 70 80 AXTAL POSITION (in.) Relative Nuclear Importance of Fuel Temperature Changes Position on an Axis Located 8.4 in. from Core Center £y UNCLASSIFIED ORNL DWG, 63-8161 RETATIVE IMPORTANCE RADIUS 15 {(in.) Fig. 3.18. Relative Nuclear Importance of Fuel Temperature Changes as a PFunction of Radial Position in Plane of Maximum Thermal Flux. RETATTVE IMPORTANCE 0.8E 0.4 UNC{ ASSIFIED ORNL DWG. 63.8162 ..... ~~~~~ ............ -10 0 10 20 30 4o 50 60 70 AXTAL POSITION (in.) Fig. 3.19. Relative Nuclear Importance of Graphite Temperature Changes as a Function of Position on an Axis Located 8.4 in, from Core Center Line. QY 46 UNCLASSIFIED ORNL DWG. 638163 RETATIVE IMPORTANCE 0 5 10 15 20 25 30 - RADTIUS (din.) Fig. 3.20. Relative Nuclear Importance of Graphite Temperature Changes as a Function of Radial Position in Plane of Maximum Thermal Flux. 477 and INOR-8 change from region to region. From the definition of these functions, the point values reflect directly the reactivity effect of & change in fuel or graphite temperature in a unit volume at that point. This occurs through changes in the local unit reaction and leakage rates, reflected in Gij of Eq. (3.3), and through variation in nuclear importance with position, reflected in ¢;¢j' Although the method presented above 1s an attempt to account approxi- mately for macroscopic variations in reactor properties with position, it should be noted the basic model is still highly idealized. The exact nature of the discontinuities in the weight functions would undoubtedly differ from those shown in Figs. 3,17-3.20, Since the reactivity change is an integral effect, however, these local differences tend to be "smeared out" in the quantities determining the operating characteristics. Consider, for example, the large increase in the fuel temperature weight- ing functions, corresponding to the region of salt plus void surrounding the control rod thimbles. This reflects both the higher average U232 concentration and the lack of graphite to dilute the effect of a salt temperature increment on the density of this region. Thus both the av- erage reaction rate and the scattering probability for neutrons entering this region are more sensitive to changes in the salt temperature. How- ever, when integrated over the volume, this region contributes only about 5% to the total fuel temperature coefficient of reactivity. The temperature coefficients of reactivity obtained from the multi- region model were in reasonably good agreement with the coefficients listed for fuel C in Table 3.4. The fuel coefficient was about 3% smaller and the graphite coefficlent about 15% smaller than those of the homoge- neous cylinder. The difference in coefficients for the graphite occurs because the wvolume of the core actually occupied by the graphite is slightly smaller than the effective "nuclear size" of the cylinder. How- ever, the validity of the assumptions concerning the space dependence of the thermal spectrum over the peripheral regions of the core is uncertain, s0 the values given in Table 3.4 are recommended as design criteria until further studies concerning these corrections can be made. 48 3.8 Reactivity Effects of Changes in Densities of Fuel Salt and Graphite Included in the category of reactivity effects of graphite and salt density changes are those due to graphite shrinkage, fuel soakup, en- trained gas, and uncertainties in measured values of the material densi- ties at operating conditions. Density coefficients of reactivity were calculated for the simplified, one-region-cylinder model of the core. In these calculations, as in the similar analysis of the temperature re- activity coefficients (Sec 3.7), lattice effects of heterogeneity were considered. The density coefficients relate the fractional change in multiplication constant to the fractional changes in densities; ok BNS ?HS The values of the coefficients, B, obtained for the three fuel salts studied are included in Table 3.5. These results directly indicate the reactivity effect of uncertainties in the measured values of the material densities. 1In order to apply the resulis to calculate the effects of graphite shrinkage and fuel soakup, some assumptions must be made con- cerning the changes in the lattice geometry produced by these perturba- tions. If shrinkage is uniform in the transverse direction across a graphite stringer, and if the center of the stringer remains fixed during contraction, the effect will be to open the gaps between stringers and allow fuel salt to enter the gaps. The homogenized density of the graph- ite remains constant; however, the effective salt density, NS, is in- creased. If vy and vg are the volume fractions of salt and graphite in the lattice, the fractional change in salt density is calculated as dvV_ = —OV (3.10) S g and v_ oV v S.S-._-E8_E&_ L | (3.11) vsvg v 49 where f; is the fractional decrease in graphite volume due to shrinkage. From Eq. (3.9), the reactivity change is ok v + = B, ;f f1 = 3.44 B_ f1 , (3.12) in which the salt/graphite volume ratio, 0.225/0.775, has been inserted. Use of the above,}elation in conjunction with the density coefficients indicates that shrinkage of the graphite by 1% of its volume corresponds to reactivity additions of about 0.65% &k/k in fuels A and C and 1.2% 8k/k in fuel B. Fuel soakup reactivity additions may also be estimated from Eq. (3.12). For this purpose the graphite shrinkage fraction fj; need only be replaced by f2, the porous volume fraction of graphite which is filled with fuel salt. 3.9 Summary of Nuclear Characteristics The nuclear characteristics of the MSRE have been calculated for three fuel mixtures, designated A, B, and C, which differ primarily in content of fuel and/or fertile material, The distinguishing features of the three fuels are as follows: fuel A contains uranium highly (~93%) en- riched in U?3% and 1 mole % thorium; fuel B contains highly enriched ura- nium but no fertile material; and fuel C contains about 0.8 mole % uranium with the U2’ enrichment reduced and no thorium. The characteristics of the reactor with each of the three fuels are summarized in Table 3.5. The uranium concentrations and inventories are listed for the initial, clean, noncirculating, critical condition and for the long-term operating con- dition. The neutron fluxes are given for the operating uranium concen- trations, and the reactivity parameters apply to the initial critical concentration. Detailed neutron balances were calculated by the computer programs for each of the three fuels, The neutron balance for the reactor filled with fuel C at the clean, critical concentration is summarized in Tables 3.6 and 3.7. Neutron absorptions and leakages associated with various portions of the reactor vessel and its contents are listed in Table 3.6. Table 3.7 gives a detailed breakdown of the neutron absorptions by ele- ment in each region of the reactor. 50 Table 3.5. Nuclear Characteristics of MSRE with Various Fuels Fuel A yel B Fuel C Uranium concentration (mole %) Clean, noncirculating ge35 0,291 0.176 0.291 Total U 0,313 0.189 0.831 Operatinga U?3 0.337 0.199 0. 346 Total U 0.362 0.214 0.890 Uranium inventory® (kg) Initial criticality U233 79 . 48 77 Total U 85 52 218 Operatinga y=3 91 55 92 Total U 28 59 233 Thermal neutron fluxes® (neutrons e~ sec”t) Maxcimum 3.31 x 1013 5.56 x 1013 3.29 x 1013 Average in graphite-moderated 1.42 x 1013 2.43 % 1013 1,42 x 1013 regilons Average in circulating fuel 3,98 x 1012 6.81 x 1012 3,98 x 10%? Reactivity coefficientsd Fuel temperature [(°F)~1] —3,03 X 1077 =4.97 x 1077 -3,28 x 10°7 Graphite temperature [(°F)~1] —=3,36 x 1077 —=4,91 x 107° —=3,68 x 10°% Uranium concentration 0.2526 0,3028 0.1754¢ 0.,2110% Xel3% concentration in core —1.28 x 108 —2,04 x 108 —1.33 x 108 (atom/barn-cm)~1 Xel3? poison fraction 0,746 -0.691 —0.752 Fuel salt density 0.190 0.345 0.182 Graphite density Q.755 0.735 0.767 Prompt neutron lifetime (sec) 2.29 x 104 3.47 X 1074 2.40 x 104 a b At operating fuel concentration, 10 Mw, d At initial critical concentration. Fuel loaded to compensate for 4% dk/k in poisons. Based on 73.2 ft? of fuel salt at 1200°F. Where units are shown, coefficients for variable x are of the form (1/k)/(dk/dx); other coefficients are of the form (x/k)/(dk/dx). e . . . s oy Based on uranium isotopic composition of clean critical reactor. TBased on highly (~93%) enriched uranium, 51 Table 3.6, Neutron Balance for Fuel C, Clean, Critical (per 10° neutrons produced) Absorptions Region g2 33 ye38 Salt® Graphite INOR Total Main coreP 45,459 7252 4364 795 1380 59,250 Upper head® 3,031 928 675 1 131 4y 766 Lower headd 1,337 449 294 0 1480 3,560 Downconmer 1,496 338 203 0 0 2,037 Core can O 0 O 0 3635 3,635 Reactor wvessel 0 0 0 0 3056 3,056 Total 51,323 8967 5536 796 9682 76,304 Leakage curface Fagt Slow Total Top 1,991 10 2,001 Sides 19,619 1004 20,623 Bottom 1,068 4 1,072 Total 22,678 1018 23,696 aConstituents other than U235 and U238, bRegions J, K, L, M, N, and T (Fig. 3.3). ®Regions D, E, G, H, Q, R, and S (Fig. 3.3). d'Regng:i_cms 0 and P (Fig. 3.3). Table 3.7. Detailed Distribution of Neutron Absorptions with Fuel C Absorptions per 10° Neutrons Produced Regiona ge3s y?38 R34 yR3é 146 1i’ Be zr F{n,x) F(n,y) GCraphite INOR Total A 0 0 0 0 0 0 0 0 0 0 324 324 B 0 0 0 0 0 0 0 2578 2,578 C 0 0 0 0 0 0 154 154 D 1,518 546 8 4 26 13 27 185 115 37 0 0 2,478 E 571 155 3 1 11 6 8 by 30 11 0 123 964 F 1,496 338 7 2 27 17 14 77 39 20 0 0 2,037 G 424 105 2 1 7 5 27 17 0 0 598 H 494 114 2 1 5 26 15 1 8 687 I 0 0 0 0 0 0 0 0 0 3635 3,635 J 42,837 6768 160 48 905 510 221 1247 517 480 762 0 54,456 K 0 0 0 0 0 0 0 0 0 0 0 1380 1,380 L 304 58 1 0 6 4 2 11 5 3 7 0 402 M 1,149 199 4 1 23 13 6 37 14 13 20 0 1,480 N 419 85 2 1 8 5 3 17 6 6 0 557 0 438 112 2 1 8 5 4 28 12 7 0 790 1,407 P 899 337 5 2 11 g 15 120 b 22 0 690 2,153 Q 19 7 0 0 0 0 2 1 0 0 0 30 R 3 0 0 0 0 0 0 0 5 S 2 0 0 0 0 0 0 0 0 0 0 3 T 750 142 3 1 15 9 5 29 13 9 0 0 976 Total 51,329 8967 199 63 1056 599 315 1850 828 621 796 %82 76,304 8 etters refer to designations in Table 3.1 and Fig. 3.3. cs 53 4, CONTROL ROD CALCULATIONS 4.1 Control Rod Geometry The MSRE control element consists basically of a hollow poison cylinder, 1.08 in. OD X 0.12 in. thick. Figure 3.2 illustrates those details of the configuration of the element which are important in de- termining the reactivity worth of the rods. Three such elements are used, located in a square array about the core center in the positions shown in Fig. 3.2. The fourth position of the array is occupied by a graphite sample assembly. 4.2 Method of Calculation of Rod Reactivity 4.2.1 Total Worth Several practical simplifications and approximations were necessary in order to estimate the reactivity worth of the control element described above. These were made in accordance with the present "state of the art" in control rod theory, reviewed in ref 17. ©Several of the computational devices used in the present studies are discussed in this report. The basic physical assumptions involved in the MSRE design calculations are as follows: a. The Gdp03-Als03 poison cylinders are assumed to be black to thermal neutrons and transparent to neutrons above thermal energies ( 21 ev). The former assumption should be excellent, since the poison material has an absorption-to-scattering ratio in excess of 10° in the thermal energy range. The latter assumption is in error, since c¢dt?® and Gd**7 resonances occur in the epithermal range, and thus have the effect of producing a "gray region" in aebsorption at these energies. Because these resonances are closely spaced and have large resonance scattering components, it is difficult to obtain meaningful estimates of the reso- nance self-shielding in the posion tube. Since the total epithermal absorption is expected to be only a fraction of that in the thermal region, this effect was neglected in the calculations. 54 b. Transmission of thermal neutrons through the INOR-8 thimbles and across the gap between thimble and cylinder was calculated using the P-1 approximation. The average absorption-to-scattering ratio for thermal neutrons traversing the INOR-8 is about 0.1. This means that diffusion theory should be adequate in calculating the thimble trans- mission, relative to the other simplifications used in the rod worth calculations. The basic mathematical relations involve the control ele- ment blackness, B, which is the probability of capture for thermal neu- trons incident on the outside surface of the thimble. This eXpression + .18 is F(p,/L) B=1- B-§TE§7ET— 5 (4.1) where B is the probability that neutrons entering the gap from the thimble miss the central poison cylinder, and pg and pg are the inner and outer radii of the thimble. The function F(x) is defined in terms of Bessel functions: To(x) + a Ko(x) + 22 I1(x) — 2> a K (x) Flx) = 2D 2D ; Io(x) + a Ko(x) — jE-Il(X) tT-@a K (x) ~ Tale,/L) "-§%~-%4§—§- To(e, /L) K1 (o, /L) +-§%—-%45—§— Ko (p /L) . In the above formulas, D and L are the thermal diffusion coefficient and diffusion length in the INOR-8. When the central poison tube 1s with- drawn, B is equal to unity. With the rod in place, Newmach's approxi- mation for B was used.l? This is based on the assumption that the angular distribution of neutrons entering the gap is correctly given by P-1 theory. For a black central cylinder, the resulting expression is l—-1r + f(r s =1 (4-2) 55 where r = pI’Od/pg 2 af R }._l | K f(r) =1 —-%— sin™ r - Equations (4.1) and (4.2) were applied to the calculation of the rod reactivity worth by the use of a linear extrapolation distance boundary condition at the control element surface. The extrapolation distance depends not only on the control element blackness, but also on 20 the relative size of the control region. The expression used was o = - 4 Mex = F/am = Mr 3BT g(DO/Atr) ’ (4.3) where n is the outward normal to the control surface and Ktr is the transport mean free path for thermal neutrons in the core. As indicated in Eq. (4.3), the function g(y) depends only on the ratio of the control radius to the transport mean free path; this function increases from zero at y = 0 to 0.623 for large y. Reference 19, p 725, gives a plot of the value of Aex/%tr vs y for black cylinders (B = 1). This was used to de- termine g(y) for thermal neutrons incident on the MSRE element. c. The remaining simplifications in the reactivity worth calcula- tions deal with the geometry of the reactor core and control rcd con- figuration. These calculations of Bk/k due to insertion of the central poison cylinders were made using the EQUIPOISE-3 program. Use of this numerical solution method, together with the practical restriction to two-dimensional calculations, required that the reactor-rod configuration be approximated in x-y geometry. The configuration used for a model is shown in Fig. 4.1l. This figure represents a horizontal cross section of the core. The basic model is that of a parallelepided with square base. The control regions are represented by regions of square cross section, with the perimeter of each square equal to the actual circumference of the control thimble. Thus the total effective absorptions of the control regions were equal in the model and the actual element. The overall transverse dimension of the core was s0 chosen that the total geometric 1 2 4 6 8 10 12 14 16 20 22 24 26 28 30 32 34 36 38 40 42 43 56 UNCLASSIFIED ORNL-DWG 63-7317 AX=MESH SIZE (cm) ' Ax= Ax=|Ax= 1.00 | 154 1 1.00 i 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 4243 Ax = AX = 1.44 5.03 AX = 1.44 Ax = 5.03 - 24.78 in. n M 5 Ll - n ~ 5 L ro B W > - -l o -~ 3 LEL 21.78 in. S = SAMPLE HOLDER Fig. 4.1L. Cross Sectional Model of MSRE Core Used in Equipoise Calculations of Control Rod Worth. 57 buckling in the transverse (x—y) dimension was equal to0 the effective radial buckling of the actual cylindrical. core. Axial leakage was ac- counted for by insertion of an effective axial buckling. Because of the limitation of the calculations to two dimensions, it was necessary to assume that the layout shown in Fig. 4.1 extended completely through the active length of the core. In actuality, the maximum penetration dis- tance for the poison cylinders is slightly less than this length. The model shown in Fig. 4.1 is based on practical limitations con- cerning the total number of mesh points in the EQUIPOISE program. The attempt was made ©o0 adjust the mesh size so that minimum error is oOb- tained in the central region of the core where the control elements are located. This is the region of maximum nuclear importance, and also that of maximum spatial flux variation when the rods are inserted. Repre- sentation of the reactor transverse boundary as a square is expected to generate relatively little error in the calculations of the total rod worth. The effect of the graphite sample holder was neglected in these preliminary calculations. Further studies are planned to examine this effect, and also to improve on some of the above approximations. 4,2.2 Differential Worth Determination of the worth of partially inserted rods is of impor- tance in setting control rod speeds, in setting limiting rod positions, and in predicting the required rod motion during stertup and normal op- eration. In keeping with the practical restriction to two-dimensional diffusion calculations, a preliminary estimate of the differential worth was based on an r—z geometry model of the core. The three control ele- ments were replaced by a single absorber shell, concéentric with the core axis. The relative change in 8k/k was calculated as a function of the venetration distance of the shell in the core. The radius and thickness of the shell were determined by equating the effective surface-to-volume ratio of the shell to that of the actual elements. The relative change in 8k/k was then normalized to the total rod worth obtained from the cal- culations described in Sec 4.2.1. 58 4.3 Results of Calculations 4.3.1 Total Reactivity Worth The total control worth of all three rods inserted all the way through the core, obtained from the calculations described in the pre- vious section, i1s listed in Table 4.1. The worth of the individual rods was also estimated for one of the fuel salts (fuel A), and the results are included in Table 4.l. When converted to represent fractions of the total worth of all three rods, these latter results should be nearly equal for all three fuel salfs. Note that the rod worths are not addi- tive, since there is appreciable "shadowing" between the rods. Also, rods 1 and 3 are worth slightly more than rod 2, due to the relatively greater influence of flux depression, caused by thimbles 1 and 3, on the position of rod 2. 4.3.2 Differential Worth Results of the r—z calculation for the partially inserted rod bank are shown in Fig. 4.2. This 1s a plot of the fraction of the total axial core height to which the rods are inserted. It is important to note that these results apply to the three rods moving as a unit; effects of moving a single rod with the others held fixed in some partially inserted posi- tion are not treated in these calculations. Table 4.1. Control Rod Worths in the MSRE . . Worth Fuel Rod Configuration (% Sk/k) A 3 Rods in 5.6 Rod 1 in, rods 2 and 3 out 2ot Rod 2 in, rods 1 and 3 out 243 Rods 1 and 3 in, rod 2 out bok Rods 1 and 2 in, rod 3 out 4.1 B 3 Rods in 7.6 C 3 Rods in 5.7 FRACTION OF TOTAL WORTH 59 UNCLASSIFIED ORNL-LR-DWG 57687A 1.0 — 0.8 f——t—— 0.6 — 0.4 [——- - o 0.2 ——- - 0 0 0.2 0.4 0.6 0.8 Fig. 4.2. FRACTION OF LENGTH INSERTED BEffect of Partially Inserted Rods. 1.0 60 5. CORE TEMPERATURES When the reactor is operated at power there is a wide range of temperatures in the graphite and fuel in the core. The temperature dis- tribution cannot be observed experimentally, but some information on the distribution is necessary for the analysis of reactivity changes during power operation. The method by which MSRE core temperatures were pre- dicted is described in detail in ref 21. The calculational method com- bines the flow distribution in a hydraulic model of the core with the power—density distribution predicted for the nuclear model. The nu- merical results presented here were computed with the power—density dis- tribution appropriate for fuel C, but calculations for fuels A and B gave practically the same results. (The numerical results in ref 17 were computed for fuel B, with a slightly different model from that used in the calculations whose results are reported here.) 5.1 Overall Temperature Distributions at Power The temperature distribution in the MSRE core can be regarded as a composite of the overall temperature distributions in the fuel and moder- ator, upon which are superimposed local temperature variations within individual fuel channels and moderator stringers. The overall tempera- ture distritutions are determined by the gross distribution of the power density and the fuel flow pattern. The local variations depend on the fluid flow and heat transfer conditions associated with the individual channels. Since the overall temperature distributions contribute most to the temperature-induced reactivity effects, these are described in detail. Details of local temperature variations are considered only where such consideration is essential to evaluating the overall distri- bution. 5.1.1 Reactor Regions A significant fraction of the nuclear power produced in this re- actor is generated in the fuel-containing regions of the reactor vessel outside the fuel-graphite matrix which forms the main portion of the 61 core. These regions contribute to the total temperature rise of the fuel as it passes through the reactor and must, therefore, be included in the core temperature calculations. The 20-region model of the re- actor (see Fig. 3.3 and Table 3.1) used for the nuclear calculations was also used to evaluate the core temperatures. The regions designated J, L, M, N, and T were combined to form the main portion of the core, and the remaining fuel-bearing regions were treated separately. Hydraulic studies on one-fifth-scale and full-scale models of the reactor vessel showed that the vertical fuel velocity varies with radial position in the main portion of the core. The velocity is nearly con- stant over a large portion of the core, but higher velocities occur near the axis and near the ocuter radius. To allow for this, three radial regions were used in calculating the temperature distributions in the main portion of the core. 5.1.2 Fuel Temperatures Nearly all of the nuclear power is removed from the reactor vessel by the circulating fuel stream, so that the fuel temperature rise and flow rate define the operating power level of the reactor. The tempera- ture calculations were based on a nominal power level of 10 Mw, with a 50°F temperature rise across the reactor and a fuel flow rate of 1200 gpm. The reactor inlet and outlet temperatures were set at 1175°F and 1225°F, respectively. These temperatures permit presentation of the distributions in abolute terms, but the shape of the distributions is unaffected by this choice. Peripheral Regions. — Approximately 14% of the reactor power is produced in or transferred to the fuel~bearing regions surrounding the main portion of the core. Since the temperature rise of the fuel, as it passes through any one of these regions, is small compared with the rise in the main portion of the core, no attempt was made to evaluate, exactly, the fuel temperature distributions in each peripheral region. Instead, the mean temperature rise for each region was calculated from the fraction of the total power produced in the region and the fraction of the total flow rate through it. The inlet temperature for each region 62 was assumed constant at the mixed-mean outlet temperature of the pre- ceding region. Fach peripheral region was assigned an approximate bulk average temperature midway between the inlet and outlet temperatures. Table 5.1 summarizes the flow rates, heat rates, and fuel temperatures in the various reactor regions. Main Portion of the Core. — The wide variations in fuel tempera- ture, both radially and axially, in the main part of the core necessitate a more detailed description of the temperature distribution. Table 5.1. Flow Rates, Heat Rates, and Temperatures in Reactor Regions® Region Flow Heat RateP Temperagure RiseP Average ?emperaturec (gom) (ko) (°F) (°F) D 1142 355.3 1.9 1225.2 E 1142 115.8 Q.6 1224.0 F 1200 378.2 1.9 1176.0 G 1142 g2.7 0.4 1223.5 H 1142 95.7 0.5 1223.0 J 1142 g121.3 4247 d L 17 59.3 20.9 d M 1183 223.0 1.1 d N 1200 84.1 0.4 d 0 1200 89.9 0.4 1178.4 P 1200 252.8 1.3 1177.6 Q 17 3.9 1.4 1201.0 R 17 0.7 0.2 1200.2 S 17 0.5 G.2 1200.0 T 41 136.9 20.0 d aRegions not containing fluel are excluded. bAt 10 Mw. Includes heat transferred to the fuel from adjoining regions. CWwith T, = 1175°F, T__. = 1225°F. in ou t dActual temperature distribution calculated for this region. See text. 63 The average temperature of the fuel in a channel at any axial posi- tion is equal to the channel inlet temperature plus a rise proportional to the sum of the heat generated in the fuel and that transferred to it from the adjacent graphite as the fuel moves from the channel inlet to the specified point. The heat produced in the fuel follows very closely the radial and axial variation of the fission power density. Since the heat production in the graphite is small, no great error is introduced by assigning the same spatial distribution to this term. Then, if axial heat transfer in the graphite is neglected, the net rate of heat addition to the fuel has the shape of the fuel power density. The fuel temperature rise is inversely proportional to the volumetric heat ca- pacity and velocity. Thus Tf(r,z) = Tf(z =0) + f(‘) w Pf(r,z) dz (5.1) where Qf is an equivalent specific power which includes the heat added to the fuel from the graphite. The channel inlet temperature, Tf(z = 0), is assumed constant for all channels, and its value is greater than the reactor inlet temperature because of the peripheral regions through which the fuel passes before it reaches the inlet to the main part of the core. The volumetric heat capacity, (pcp)f, is assumed constant, and only radial variations in the fuel velocity, u, are considered. It is further assumed that the radial and axial variations in the power-density distribution are separable: P(r,z) = A(r) B(z) . (5.2) Then (Qf)m A(r) z (pcp)f u(r) J; B(z) dz . (5.3) Tf(r,z) = Tf(z = 0) + If the sine approximation for the axial variation of the power density (Fig. 3.10) is substituted for B(z), Eq. (5.3) becomes (z =0) + Kifl‘%{cos o — cos [?e?jli'é’” (z +5.72)N> . (5.4) Tf(r,z) = T, 64 In this expression, k is a collection of constants, 78.15 (Qf)m J T (pcp)f (5.5) K= and 0 (0 + 5.72) . (5.6) _ T 78.15 The limits within which Eq. (5.4) is applicable are the lower and upper boundaries of the main part of the core, namely, 0 = z = 64.6 in. It is clear from this that the shape of the axial temperature distribu- tion in the fuel in any channel is proportional to that of the central portion of the general curve [1 — cos B]. The axial distribution for the hottest channel in the MSRE is shown in Fig. 5.1, where it is used to provide a reference for the axial temperature distribution in the graphite. The radial distribution of the fuel temperature near the core mid=- plane is shown in Fig. 5.2 for the reference conditions at 10 Mw. This distribution includes the effects of the distorted power-density distri- bution (Fig. 3.11) and the radial variations in fuel velocity. At the reference conditions the main core inlet temperature is 1179°F and the mixed-mean temperature leaving that region is 1222°F. The additional heat required to raise the reactor outlet temperature to 1225°F is produced in the peripheral regions above the main part of the core. The general shape of the radial temperature profile is the same at all axial positions in the main portion of the core, 5.1.3 Graphite Temperature Since &11 of the heat produced in the graphite must be transferred to the circulating fuel for removal from the reactor, the steady-state temperature of the graphite is higher than that of the fuel in the ad- jacent channels. This temperature difference provides a convenient means of evaluating the overall graphite temperature distribution; that is, by adding the local graphite-fuel temperature differences to the previously calculated fuel temperature distribution. 65 UNCLASSIFIED ORNL DWG. 63.8164 1300 1280 1260 1240 1220 TEMPERATURE (°F) 1200 1180 1160 0 10 20 30 4o 50 0 70 AXTAL POSITION (in.) Fig. 5.1. Axial Temperature Profiles in Hottest Channel and Adja- cent Graphite Stringer. Nearly all the graphite in the MSRE (98.7%) is contained in the regions which are combined to form the main portion of the core. Since the remainder would have only a small effect on the system character~ istics, the graphite temperature distrivbution was evaluated for the main part of the core only. Local Graphite-Fuel Temperature Differences. — In order to evaluate the local graphite-fuel temperature differences, the core was considered in terms of a number of unit cells, each containing fuel and graphite. Axial heat transfer in the graphite was neglected and radially uniform 1280 1280 1270 1260 1250 1240 1230 TEMPERATURE (°F) 1220 1210 1200 1190 1180 Fig. 5.2. 66 UNCLASSIFIED ORNL DWG. 63-8165 5 0 15 20 25 30 RADIUS (:n.) Radial Temperature Profiles Near Core Midplane. 67 heat generation terms were assumed for the fuel and graphite in each cell. In general, only the difference between the mean temperatures of the graphite stringers and fuel channels was calculated as a function of radial and axial position. The difference between the mean graphite and fuel temperatures in a unit cell can be broken down into three parts: 1. +the Poppendiek effect, which causes the fuel near the wall of a channel to be hotter than the mean for the channel; 2. the temperature drop due to the contact resistance at the graphite- fuel interface; and 3. the temperature drop in the graphite resulting from the internal heat source. When a fluid with an internal heat source flows through a channel, the lower velocity of the flulid near the channel wall allows that part of the fluid to reach a temperature above the average for the channel. This effect 1s increased when heat is transferred into the fluid through the channel walls, as is the case in the MSRE. Equations have been developedzz’23 to evaluate the difference between the temperature of the fluid at the wall and the average for the channel. These equations were applied to the reactor, assuming laminar flow in all of the channels. This tends to overestimate slightly the temperature rise in the few channels where the flow may be turbulent. No allowance was made for a temperature difference due to the con- tact resistance at the graphite-fuel interface in these calculations. An estimate of this resistance was made by assuming a l-mil gap, filled with helium, between the graphite and fuel. This rather pessimistic assump- tion led to a temperature difference which was very small compared with the total. The difference between the mean temperature of a graphite stringer and the surface temperature was calculated for two simplified geometries: a cylinder with a cross-sectional area equal to that of a stringer and a slab with a half thickness equal to the normal distance from the center of a stringer to the surface of a fuel channel. The value assigned to 68 the graphite was obtained by linear interpolations between these results on the basis of surface-to-volume ratio. The local graphite-fuel temperature difference was calculated as a function of position in the core for three degrees of fuel soakup in the graphite: 0, 0.5, and 2.0 vol % of the graphite. In each case, uniform distribution of the fuel within the graphite was assumed. Table 5.2 gives the maximum difference between mean stringer and mean fuel channel temperatures for the three conditions. The distribution of the fuel soaked into the graphite has little effect on the total temperature dif- ference. For 2 vol % permeation, concentration of the fuel near the outer surface of the graphite increased the AT by 2°F. Table 5.2. Maximum Values of Graphite-Fuel Temperature Difference as a Function of Fuel Permeation Fuel Permeation (vol % of graphite) 0 0.5 2.0 Graphite-fuel temperature difference (°F) Poppendiek effect in fuel 55.7 58.3 65 4 Graphite temperature drop 5.5 6.7 9.8 Total 6L.2 65.0 75.2 Overall Distribution. — Since the Poppendiek effect and the tempera- ture drop through the graphite are both influenced by the heat generated in the graphite, the spatial distribution of the graphite temperature is affected by the graphite power-density distribution. The graphite power density is treated in detail in Sec. 1l4.1, for fuel C with no fuel per- meation of the graphite. The distribution shown in Figs. l4.1 and 14.2 was used to evaluate the graphite temperatures in Figs. 5.1 and 5.2. Figure 5.1 shows the axial distribution of the mean temperature in a graphite stringer adjacent to the hottest fuel channel. Because of the continuously increasing fuel temperature, the axial maximum in the graph- ite temperature occurs somewhat above the midplane of the core. The 69 overall radial distribution of the graphite temperature near the core midplane is shown in Fig. 5.2. 5.2 Average Temperatures at Power The concept of average temperatures has a number of useful applica- tions in operating and in describing and analyzing the operation of a reactor. The bulk average temperature, particularly of the fuel, is essential for all material balance and inventory calculations. The nu- clear average temperatures of the fuel and graphite, along with their respective ftemperature coefficients of reactivity, provide a convenient means of assessing the reactivity effects associated with temperature changes. Both the bulk average and nuclear average temperatures can be described in terms of the reactor inlet and outlet temperatures, but, because of complexities in the reactor geometry and the temperature dis- tributions, the numerical relations are not obvious. 5.2.1 Bulk Average Temperatures Bulk average temperatures (f) were obtained by weighting the overall tempersture distributions with the volume fraction of salt or graphite and integrating over the volume of the reactor. The fuel bulk average temperature was calculated for the fuel with- in the reactor vessel shell. (The contents of the inlet flow distributor and the outlet nozzle were not included.) A large fraction of the salt in the vessel is in the peripheral regions, where detailed temperature distributions were not calculated. In computing the average for the re- actor, average temperatures shown in Table 5.1 were used for these re~ gions. The average temperature in the main part of the core was computed by numerical integration of the calculated temperature distribution. At the reference condition (1175°F inlet, 1225°F outlet), the fuel bulk average temperature for all of the fuel in the reactor vessel was com- puted to be 1199.5°F. Thus, assuming linear relationships, the fuel bulk average temperature is given by T, = Tin + O.49(Tout — Tin) . (5.7) 70 Only the graphite in the main portion of the core had to be included in the calculation of the graphite bulk average temperature, since this region contains 98.7% of all the graphite. For fuel C with no permeation, the bulk average graphite temperature at the 10-Mw reference condition is 1229°F. This temperature increases with increasing permeation of the graphite by fuel; earlier calculations of this effect showed a 4.4°F in- crease in graphite bulk average temperature as the fuel permeation was increased from O to 2%. 5.2.2 Nuclear Average Temperatures The nuclear average temperatures (T*) of the fuel and graphite were calculated in the same way as the bulk average temperatures, except that the temperature distributions were weighted with their respective nuclear importances as well as with the amounts of material. The temperature weighting functions described in Sec. 3.7.2 include all of the nuclear average weighting factors. These functions were applied to the fuel temperature distribution and resulted in a fuel nuclear average tempera- ture of 1211°F when the inlet temperature is 1175°F and the outlet is 1225°F, With the same inlet and outlet temperatures and no fuel per- meation, the graphite nuclear average temperature was calculated to be 1255°F. (With 2% permeation the calculated graphite nuclear average temperature would be higher by 7°F.) The relations between inlet and outlet temperatures, nuclear average temperatures, and power are all practically linear so that the following approximations can be made: out = iy + 50 P, (5.8) * Tout * Tin Tp=|—————|+L1P=T_, —1.4P, (5.9) Tout i Tin T; = |———— ] +55P=1T . +3.0P, (5.10) where the temperatures are in °F and P is the power in Mw. 71 5.3 Power Coefficient of Reactivity Whenever the reactor power i1s raised, temperatures of the fuel and graphite throughout the core must diverge. As shown in the preceding sections, the shape of the temperature distributions at power and the relations between inlet, outlet, and average temperatures are inherent characteristics of the system which are not subject to external control. The relation of the temperature distribution at high power to the temper- ature of the zero-power, isothermal reactor, on the other hand, can be readily contreclled by the use of the control rods. When the reactivity effect of the rod poisoning is changed, the entire temperature distribu- tion 1is forced to shift up or down as required to produce an exactly compensating reactivity effect.* Normally the rods are adjusted concur- rently with a power change, to obtain a desired temperature behavior (to hold the outlet temperature constant, for example). The ratio of the change in rod peisoning effect, required to obtain the desired result, to the power change is then called the power coefficient of reactivity.** Because of the way in which the nuclear average temperature 1s de- fined, the effect of fuel temperature changes on reactivity is proportional to the change in the nuclear average temperature of the fuel. Reactivity effects of graphite temperature changes are similarly described by the change in graphite nuclear average temperature. The net effect on reac- tivity of simultanecus changes in fuel and graphite temperature 1s LK * * = AT+ 0 AT (5.11) where Q% and ag are the fuel and graphite temperature coefficients of reactivity. The change in rod polsoning is equal in both sign and magnitude to the reactivity effect of the temperature changes. (If the *This statement and the discussion which follows refer to adjust- ments in rod positions and temperatures which are made in times too short for significant changes in other reactivity effects, such as xenon poisoning. **Note that the power coefficient does not have a single value, as does a coefficient like the temperature coefficient, because its value depends on the arbitrary prescription of temperature variation with power., 72 effect of the desired temperature change is to decrease the reactivity, the rod poisoning must be decreased an equal amount to produce the tem- perature change.) Thus Eq. (5.11) can be used to evaluate the power coefficient of reactivity. When Egs. (5.9) and (5.10) for Tg and Tg are substituted, Eq. (5.11) becomes either AR —— .(x—.a » = (Qé + a%)amout + (3.0 : 1.4 f)AP (5.12) or T + T Ak out in = = —_ T OO e . . = (o% + a%)a,( 5 ) + (5.5 - 1.1 f)AP (5.13) If T, 18 held constant during power changes (i.e., if AT L 18 Zero), the power ccoefficient is Ak/k = 3,008 — 1.4 ., . —5 3.0 . 1.4 ap (5.14) Similarly, if the mean of the inlet and outlet temperatures is to be held constant, Nk /k —_ . a . e A 5.5 ag + 1.1 - (5.15) If there is no adjustment of reactivity by the control rods, the temperatures must change with power level in such a way that Ak/k is zero. (This mode of operation might be called "hands-off" operation, because the rods are not moved.) The power coefficient of reactivity in this case is by definition equal to zero. The change in temperatures from the zero-power temperature, Tg, is found from ékE = o ATY + cngT; =0, (5.16) 0L (T — Tg) = —G%(T;-— Ty) « (5.17) 73 In conjunction with (5.9) and (5.10), this leads to o Yoty aé r - -0 O, + aé P, (5.18) T = Ty + ;i:iiff__ P (5.19) g Q% + Q% ? 3.0 0 - 1.4« o x T " g Note that the changes with power depend on the values of af and ag’ hence on the type of fuel in the reactor. Thus it has been shown that the power ccefficient of reactivity de- pends on the type of fuel and also on the chosen mode of control. Table 5.3 lists power coefficients of reactivity for three fuels and three modes of control. Also shown are temperatures which would be reached at 10 Mw if the zero-power temperature were 1200°F. Table 5.3. Power Coefficients of Reactivity and Temperatures at 10 Mw Power Coefficient Temperaturesa o Mode of Control (% Bk/k) Mo ( F) Fuel A Fuel B Fuel C T T, ™ out in f g Constant Tout —0.006 -0.008 —0.006 1200 1150 118 1230 T o+ T, COnstant——‘?flz—m —0.022 —-0.033 —0.024 1225 1175 1211 1255 "Hands-off" Fuel A O 1191 1141 1177 1221 Fuel B 0 1192 1142 1178 1222 Fuel C Q 1191 1141 1177 1221 “System isothermal at 1200°F at zero power. T4 ©. DELAYED NEUTRONS The kinetics of the fission chain reaction in the MSRE are influ- enced by the transport of the delayed neutron precursors. An exact mathematical description of the kinetics would necessarily include, in the equation for the precursor concentrations, terms describing the movement of the precursors through the core and the external loop. In order to render the system of kinetics equations manageable, the trans- port term was omitted from the equations used in MSRE analysis (see Sec 12.4.1). Thus the equations which were used were of the same form as those for a fixed-fuel reactor. Some allowance for the transport of the delayed neutron precursors was made by substituting "effective" values for delayed neutron yields in place of the actual yields. The kinetics calculations used "effective" yields equal to the contributions of the delayed neutron groups to the chain reaction under steady-state conditions. 6.1 Method of Calculation In the calculation of the effective contributions during steady power coperation, nonleakage probabilities were used as the measure of the relative importance of prompt and delayed neutrons. Spatial distri- butions for the precursors during steady operation were calculated and were used, together with the energy distribution, in computing nonleakage probabilities.?% The MSRE core was approximated by a cylinder with the flux (and precursor production) vanishing at the surfaces. Flow was assumed to be uniformly distributed. With these assumptions, the spatial distribution of precursors of a particular group in the core was found to be of the form -A\t_z/H + [Sl sin %; - 52 cos-%?— + Sse ¢ ] Jo (?}gf) . (6.1) (See Sec 6.4 for definition of symbols.) 75 For the purpose of computing nonleakage probabilities, the spatial distribution of each group was approximated by a series: v o jmr ’IITZ s(r,z) = L Y Amdo <—R—> sin(é ) . (6.2) m=1 n=1 The coefficients, Amn’ were evaluated from the analytical expression for S(r,z). The nonleakage probability for a group of neutrons was then computed by assigning a nonleakage probabllity to each term in the series equal to (6.3) where 3N\ ' 2 2 [ B nr BZ ( = ) +< H) . (6.4) The energy distribution of each delayed neutron group was taken into account by using an appropriate value for the age, 7, in the expression for the nonleakage probability. 6.2 Data Used in Computation 6.2.1l Precursor Yields and Half-ILives The data of Keepin, Wimett, and Zeigler for fission of U?3° by thermal neutrons were used.?’ Values are given in Table 6.1. 6.2.2 Neutron Energies Mean energies shown in Table 6.1 for the first five groups are values recommended by Goldstein.?® A mean energy of 0.5 Mev was assumed for the shortest-lived group, in the absence of experimental values. 6.2.3 Age Prompt neutrons, with an initial mean energy of 2 Mev, have an age to thermal energies in the MSRE core of 292 cm? (this value was computed by a MODRIC multigroup diffusion calculation). The age of neutrons from the different sources was assumed to be proportional to the lethargy; that is, log (E,/E.. ) = v T . (6.5) i ~ log (Epr/Eth) pr T Computed values of T, are given in Table 6.1, Table 6.1. Delayed Neutron Data Group 1 2 3 4 5 6 Precursors half-life (sec) 55.7 22.7 6422 2.30 0.61 0.23 Fractional yield of 2.11 14.02 12.54 25.28 7 40 2.70 precursors, 1048, (neutrons per 104 neutrons) Neutron mean energy (Mev) 0.25 0.46 0.40 0.45 0.52 0.5 Neutron age in MSRE (ecm®) 256 266 264 266 269 268 6.2.4 MSRE Dimensions The computation of B* for the nonleakage probabilities used R = 27.75 in. and H = 68.9 in. The volume of fuel within these boundaries is 25.0 ft2?. At a circulation rate of 1200 gpm, residence times are 9.37 sec in the core and 16.45 sec in the external loop. A thermal neutron diffusion length appropriate for a core with highly (~93%) enriched uranium and no thorium was used (L? = 210 cm?®). 6.3 Results of Computation The core residence time, in units of precursor half-lives, ranges from 0.2 to 4l. Because of this, the shapes of the delayed neutron sources in the core vary widely, as shown in Fig. 6.1, when the fuel is circulating. (The source strength is normalized to a production rate of 77 UNCLASSIFIED ORNL-LR-DWG 73620R (x1079) 2.8 l GROUP f'/z (sec) { 56 > 4 2 23 ' 3 o.2 4 2.3 5 0.6 >0 o J 0.2 (SEE FIG 6.2 FOR GROUP 4 DISTRIBUTION) 1.6 .2 / / \ ) 0.8 / S \ I . . 1 O 0.2 0.4 0.6 0.8 {.0 RELATIVE HEIGHT Fig. 6.1. Axial Distribution of Delayed Neutron Source Densities in an MSRE Fuel Channel. Fuel circulating at 1200 gpm. RELATIVE DELAYED NEUTRON SOURCE DENSITY (cm~—3) N 78 1 neutron/sec in the reactor.) Figure 6.2 compares source distributions for one group under circulating and static conditions. The reduction in the number of neutrons emitted in the core is indicated by the difference in areas under the curves. A greater probability of leakage under circu- lating conditions is suggested by the shift in the distribution, which reduces the average distance to the outside of the core. Table 6.2 summarizes important calculated quantities for each group. The total effective fraction of delayed neutrons is 0.00362 at a 1200-gpm circulation rate and is 0.00666 in a static core. The total yield of precursors is 0,00641. Table 6.2. Delayed Neutrons in MSRE at Steady State Group 1 2 3 4 5 6 Circulating: 0, 0.36 0.37 0.46 Q.71 0.96 0.99 P, /P 0.68 0.72 0.87 0,91 1.00 1.03 1’ pr * B:/Bs 0.25 0.27 0.40 0.e7 0.97 1.02 104B§ 0.52 3.73 4,99 16.98 7.18 2.77 Statics P, /Ppy 1.06 1.04 1.04 1.04 1.03 1.03 1o4a§ 2.23 1l4.57 13.07 26.28 7 .66 2.80 6.4 Nomenclature for Delayed Neutron Calculations Amn Coefficient in series representation of S B? Geometric buckling B Initial mean neutron energy Eth Thermal neutron energy H Height of core 79 UNCLASSIFIED ORNL -LR-DWG 73621 (x1079) o 7 TN\ 5 5 / \ > / \ % /STATIC \ S, / A O / 7\ / / \ S 3 / \ ; / /lRCULATlNG \ o 2 / / \ < // \ R \ g // / \ 5 \ o V \ O O 0.2 0.4 0.6 0.8 1.0 RELATIVE HEIGHT Fig. 6.2. Effect of Fuel Circulation on Axial Distribution of Source Density of Group 4 Delayed Neutrons. TFuel circulating at 1200 gpm. Jo 80 Bessel function of first kind mth root of Jg(x) = O Neutron diffusion length Nonleakage probability Radial distance from core axis Qutside radius of core Neutron source per unit volume of fuel Residence time of fuel in core Axial distance from bottom of core Fractional yield of neutrons of group 1 Effective fraction of neutrons of group i Fraction of group 1 emitted in core Precursor decay constant Neutron age 81 7. POISONING DUE TO XENON~135 Changes in the concentration of Xel3? in the core produce changes in reactivity that are about as large as those from all other factors combined.* In order to use the net reactivity behavior during power oOp- eration to observe changes in such factors as burnup, fuel composition, and graphite permeation, the xenon poisoning must be calculated quite ac- curately from the power history. 7.1 Distribution of Iodine and Xenon The first step in calculating the xenon poisoning is to calculate the behavior and distribution of I'3% in all parts of the reactor. (This information is, of course, necessary because most of the Xel?? is formed by decay of I135,) From this one proceeds to calculate the concentration of Xel?? in the fuel salt, in various parts of the graphite, and elsewhere throughout the reactor. A number of production and destruction mechanisms for both xenon and iodine which involwve the chemical and physical behavior of the isotopes can be postulated and described mathematically, at least in principle. Some of these mechanisms can be eliminated immediately as insignificant, while others can be shown to be highly significant., There remain, how- ever, a number of mechanisms whose significance probably cannot be evalu- ated until after the reacfior hag been operated and the operation carefully analyzed. 7.1.1 Sources of Iodine and Xenon in Fuel The only significant source of T135 in the circulating fuel is the direct production from fission; the iodine precursors in this chain have half-lives t00 short to have any significant effect. The principal sources of Xel33 in the fuel are the decay of I'3? in the fuel and direct production from fission., However, a third potential source exists 1f iodine is trapped on metal surfaces in the primary loop, *See list of reactivity shim requirements, Table 9.1. 82 and the xenon formed by the decay of this iodine does not immediately re- turn to the circulating stream, In this case, the xenon must be treated separately from that produced by decay of ilodine in the circulating stream, because the delay in the return of the xenon to circulation changes the destruction probabilities. 7.1.2 Removal of Iodine and Xenon from IFuel The principal removal mechanism for iodine is radloactive decay. However, consideration must also be given to the possibility of iodine migration into the graphite and to metal surfaces, If these processes occur, they will modify the overall xenon behavior. Volatilization or stripping of iodine in the pump bowl and destruction by neutron capture are both regarded as insignificant. There are a number of competing mechanisms for the removal of Xenon from the fuel., The most important of these are stripping in the pump bowl and migration to the graphite. Of lesser importance, but still sig- nificant, are decay of and neutron capture by xenon in the fuel itself. Decay of xenon trapped on metal surfaces must also be considered. 7.1.3 Sources of Iodine and Xenon in Graphite Unless permeation of the graphite by fuel occurs, the only source of iodine in the graphite is migration from the fuel. If fuel permeation does occur, the direct production of iodine in the graphite by fission must be considered. The major source of xenon in the graphite is migration from the fuel., Other sources which may or may not be important are decay of iodine in the graphite and direct production from the fission of fuel soaked into the graphite. 7.1.4 Removal of Iodine and Xenon from Graphite Because of the low neutron absorption cross section of 1135, the only mechanism for its removal from the graphite is by radiocactive decay to Xel3?, 1In the case of xenon, both decay and neutron capture are im- portant. 83 In all cases where the transfer of an isotope from one medium to another is involved, only the net transfer need be considered; therefore, these can be regarded as one-way processes, with the direction of trans- fer being indicated by the sign of the term. 7.1.5 Detailed Calculations A get of simultaneous differential equations has been developed to describe, in mathematical terms, all of the mechanisms discussed above, These equationg also take into account radial and axial variations in the fuel flow pattern throughout the core and within individual fuel channels, as well as the owverall distribution of the neutron flux. The equations can, theoretically at least, be programmed for solution by a large com- puter to give detailed spatial distributions of iodine and xenon in the core. An actual solution of the equations requires detalled information about a number of the chemical and physical parameters of the system, vhich is not currently available. However, some qualitative comments can be made about the nature of the results that can be expected. The digtribution of xenon in the fuel within the core will probably be relatively uniform, because of the mixing in the external loop and the fact that most of the xenon is produced from iodine that was formed in earlier passes through the core. Some depletion may occur along the re- gion near the centerline of the core, because of the higher neutron flux and because the higher fuel turbulence facilitates transfer to the graph- ite. However, the mixed-mean concentration at the core outlet must be somewhat higher than at the inlet to allow for stripping in the pump bowl and decay in the external loop. The overall radial distribution of xenon in the graphite may exhibit a minimum, due to burnout, at the radius corresponding to the maximum in the thermal flux. This minimum is reinforced by the fact that the flux maximum occurs in the low-velocity region of the core, where transfer from the fuel is slowest. In the axial direction, the highest xenon con- centrations will probably occur near the inlet to the core; the neutron flux is low in this region, and turbulence near the entrance of the fuel channels tends to promote transfer from the fuel. This distribution may, however, be significantly affected by axial diffusion in the graphite stringers. 84 7.1.6 Approximate Analysis In order to provide a bagis for estimating the reactivity effect of Xel35 in the reactor, an approximate analysis of the steady-state xenon distribution was made.?’ For this approach, the scope of the problem was reduced to include only the major behavior mechanisms. It was assumed that all of the iodine remains with the fuel in which it is produced; this completely eliminated iodine from the steady-state mathematical ex- pressions. The core was divided into four radial regions on the basis of fuel velocity, and an overall mass-transfer coefficient was calculated for xenon transfer from fuel to graphite in each region. Axial varia- tiong in xenon concentration in both fuel and graphite were neglected. Average xenon burnup rates were calculated on the basis of the average thermal neutron flux in the reactor. Fuel permeation of the graphite was neglected. Because of uncertainties in the physical parameters, the xenon be- havior was calculated for relatively wide ranges of the following vari- ables: 1. Stripping efficiency in the pump bowl. The ultimate poisoning effect of the xenon is most sensitive to this quantity, which also has the greatest degree of uncertainty associated with it. The entire range, from O to 100% efficiency, was considered. 2. Fuel-to-graphite mass-transfer coefficient. This quantity can be calculated with reasonable confidence but the xenon poisoning is rel- atively sensitive to the results. Values differing by a factor of 2 from the expected value were considered. ' 3., Diffusion coefficient for xenon in graphite., The uncertainty associated with this quantity is quite large but its effect on the poi- soning, within the range of expected values, is small., Two values, dif- fering by a factor of 100, were considered. The xenon poisoning is determined primarily by tThe xenon which dif- fuses into the graphite. Nearly all of the xenon that does not migrate to the graphite is stripped out in the pump bowl, leaving only a small fraction (<1% of the total) to be destroyed by neutron absorption or radioactive decay in the fuel. The xenon migration to the graphite is 85 not significantly affected by the choice of fuel, because all three fuels have similar physical properties. However, the choice of fuel has some effect on the poisoning, because this determines the flux level in the reactor at design power (see Table 3.5). This is illustrated by the fact that 49% of the Xel2” that enters the graphite is destroyed by neutron absorption at the flux level associlated with 10-Mw operation with fuels A and C, whereas 62% is destroyed by this mechanism with fuel B. Figure 7.1 illustrates the effect of stripping efficiency on the fraction of Xel?? produced in the reactor which migrates to the graphite. This figure also shows the effect of changing the diffusion coefficient, D, in the graphite by a factor of 100. It is expected that the average value of the graphite diffusion coefficient in the MSRE will be between the values shown. Figure 7.2 shows the effects of increasing and de- creasing the mass-transfer coefficient, K, by a factor of 2 from the ex- pected value, Kg. The curves in Fig. 7.2 are based on the higher of the two graphite diffusion coefficients, 7.2 Reactivity Effects of Xenon-135 Once the spatial distribution of xenon in circulation and that re- tained on the graphite has been calculated, it is possible to relate theo- retically the xenon reactivity effect to the poison distribution. This relation is most conveniently expressed in terms of a reactivity coeffi- cient and an importance-averaged xenon concentration.?® The method for calculating these quantities is similar to that used in obtaining the re- activity effect of temperature (Sec 3.7). In the case of xenon, however, the weight function for the poison concentration is proportional to the product ¢§¢2: * a * . j;raphite iy, 922 av, + Joars Tge02%2 avy : Ny, = T % s 7.1) reactor b202 AV * where Nke is the importance-averaged concentration per unit reactor vol- ume , and N%e and Nie are the local concentrations, per unit volumes of * graphite and salt, respectively. The quantity NXe 1s also the uniform 86 UNCLASSIFIED ORNL DWG. 63-8166 FRACTION OF Xe'l>” MIGRATING TO GRAPHITE (%) 0 20 40 &0 80 100 STRIPPING EFFICIENCY (%) Fig. 7.1, Effect of Stripping Efficiency and Graphite Diffusion Coefficient on Xenon-135 Migration to Graphite. 87 UNCLASSIFIED ORNL DWG. 63-8167 100 80 70 Lo - FRACTION OF Xe > MIGRATING TO GRAPHITE (%) 30 20 10 Q 20 ho 60 80 100 STRIPPING EFFICIENCY (%) Fig. 7.2. Effect of Mass-Transfer Coefficient on Xencon-135 Migra- tion to Graphite. 88 equilibrium concentration of xenon in the reactor, which produces the same reactivity change as the actual distribution. In relating N;é to the total reactivity change, it is convenient to define a third quantity, the effective thermal poison fraction, P;e. This is the number of neu- trons absorbed in xenon per neutron absorbed in U235, weighted with re- spect 10 neutron importance : * P* “Xe j;eactor P2%2 AV N* (7.2) Xe - | (Nps0256501 + Nasa3500s) av 2 ' resctor ‘25017 F1¥L 25 2%2 where Nps5 = concentration of U235, per unit reactor volume, a{fg = 7Je35 microscopic absorption cross section for fast (1) and thermal (2) neutrons, a. Yo xenon thermal absorption cross section. * The relation between total xenon reactivity and PXe is given by28 - _ P, . (7.3) * * (8k) j;Eactor (N250%%0101 + Na505°0292) AV * oK * _ Xe (VEpp 9101 + vEFp9105) AV Xe j;eactor Thus, if knowledge of the xenon distribution can be obtained from separate experiments or calculations, the calculation of the total Xenon reactivity involves three steps: (a) obtaining N;é from Eq. (7.1), (b) calculating P;e from N;e by use of Eq. (7.2), and (c) calculating 8k/k from Eq. (7.3). Alternatively, the above relations may be used in a reverse manner if knowledge of the distribution is inferred from reactivity measurements at power. The numerical values of the xenon reactivity coefficients obtained for the three fuels under consideration are given in Table 3.5. Both the coefficients relating dk/k to the poison fraction and to the importance- averaged xenon concentration are listed. Xenon concentrations calculated by the approximate method described in Sec 7.1.6 were used with the reactivity coefficients to obtain esti- mates of the xenon poisoning in the MSRE., Since the simplified analysis used only the average neutron flux, the calculated xenon concentrations 89 were space-independent and, therefore, independent of the importance- weighting functions. (The weighted average of a constant function is the same constant, regardless of the shape of the weighting function.) It may be noted that peaking in the xenon distribution toward the center of the core would make the importance-weighted average concentrations higher than the calculated values, while peaking toward the outside of the core would have the opposite effect. Xenon reactivity effects were calculated for all three fuels; the results are listed in Table 7.1. The expected values are based on a graphite diffusion coefficient of 1.5 X 1077 ftz/hr and the calculated mass-transfer coefficients. The minimum and maximum values were obtained by applying the most favorable and unfavorable combinations of these two variables, within the limits discussed in Sec 7.1.6., The reactivity ef- fects for fuels A and C are the same because the average thermal fluxes are the same and the reactivity coefficients do not differ within the accuracy of these calculations. The higher reactivity effect with fuel B is ©to be expected, because of the higher flux associated with this mix- ture. Changes in pump bowl stripping efficiency would have the same rel- ative effect on fuel B as is shown for fuels A and C. Table 7.l. Reactivity Effects of Xel33 Fuel A or C Fuel B Pump bowl stripping efficiency (%) 25 50 1.00 50 Reactivity effect (% 8k/k) Expected -1.2 0,7 0.5 0.9 Minimum —1.0 0.5 0.3 0.5 Maximum —1.7 —1.2 ~0.9 -1.5 20 8. POISONING DUE TO OTHER FISSION PRODUCTS Many fission products other than Xel?? contribute appreciably to the neutron absorptions in the reactor after long operation at high power. There are a few stable or long-lived fission products with high cross sec- tions, the most important of which is amt4?, The poisoning effect of this group of fission products saturates in a period of a few weeks or months, but undergoes transients following power changes. In addition, there is a slowly rising contribution to the poisoning from lower-cross-section nuclides which continue to build up throughout power operation. 8.1 Samarium-149 and Other High-Cross-Section Poisons Samarium-149 is the next most important fission product poison after Xe135, having a yield of 00,0113 atom/fission and a cross section of about 40,000 barns. Unlike Xe*??, it is a stable nuclide, so that once the re- actor has been operated at power, some St 42 poison will always be present. The poison level changes, however, following power changes. Samarium-149 is the end product of the decay chain 149 Nd149 _@__; Pm149 _5_3.L_1._'-h_.> om (stable) , For all practical purposes the effect of Ndl4° on the time behavior of sm14? can be neglected., If it is further assumed that there is no direct yield of Sml%%, and no burmup of Pml%%, the equations governing the Sm'4® concentration are These equations can be solved to obtain the poisoning, P, due to the Sl 42 in a thermal reactor: V%en MenTsm Zp 2y Ty Iy g i 91 The reactivity effect of the Sml4° is simply related to P, in the case of a thermal reactor, by where f is the thermal utilization factor in the core. Figures 8.1-8.3 show the type of behavior which can be expected of the Sml%® effect in the MSRE, Figure 8.1 shows the transient following a gtep increase to 10 Mw from a clean condition. The steady-state poison- ing is independent of power level, but the rate of buildup is a function of the power, in this situation. This curve was calculated using ¢ = 1 X 1013, O = % X 10%, y = 0,0113, and fXF/EU = 0.8. When the power is re- duced the sml%® builds up, because the rate of production from ml4? ge- cay 1ls temporarily higher than the burnup of Smt4?, Figure 8.2 shows the reactivity transient due to S buildup after a reduction to zero power from the steady state approached in Fig., 8.1. After the smt4? has built up to steady state at zero power, a step increase back 1o 9 = 1 x 10%°3 results in the transient shown in Fig. 8.3. In addition to the simple production of Smt4? through Pm14?, some may be produced by successive neutron captures and beta decays in a chain beginning with Pnl47, This source can become important after a long time at a high flux, Other high-cross-section poisons which are important are Sml’l, qdl??, Gal37, Eul’%, and 0d1l3. The effect of these nuclides amounts to about 0.2 of that of the sm'*?, and saturates in roughly the same length of time. Some of these fission products have relatively short-lived parents, so that they undergo transients similar to sm'4? after changes in power, 8.2 Low-Cross-Section Poisons The large majority of the fission products may be regarded as an ag- gregate of stable, low-cross~section nuclides, The effective thermal cross section and resonance integral of this aggregate depend in an in- volved menner on the energy spectrum of the flux, the fuel nuclide, and the amount of fuel burnup which has occurred.??: 30 At 1low fuel burnup, in a thermal reactor fueled with U235, a good approximation 1s that each UNCLASSIFIED QORNL DWG. 63.8168 92 TIME {days ) t ¢ = 1 x 1013 After Startup with Clean isoning a am14? Po Fig. 8.1. Fuel. dk/k (%) 1.02 1.00 0.96 0.9 0.92 0.9 _ Fig. 8.2, at o = 1 x 1013, UNCLASSIFIED ORNL DWG, 63-8169 TIME {(days ) sml%® Poisoning at Zero Power After Reaching Steady State €6 5k/x (%) 1L.00 0.98 0.9 0.94 0.90 UNCLASSIFIED ORNL DWG. 638170 1 2 3 i 5 6 T 8 TIME (days } Fig. 8.3. om'%Y Poisoning After Step to ¢ = 1 x 101? from Peak Low-Power Poisoning. 76 - 95 fission produces one atom with a cross section of 43 barns and a reso- nance integral of 172 barns.°t In a predominantly thermal reactor with a thermal flux of 1 X 10%?, the poisoning effect of this group of fission products increases initially at a rate of about 0.003% 8k/k per day. 96 9. EMPLOYMENT OF CONTROL RODS IN OPERATION The control rods are used to make the reactor subcritical at times, to regulate the nuclear power or fuel temperature, and to compensate for the changes in reactivity which occur during a cycle of startup, power operation, and shutdown. The manner in which the control rods are em- ployed is dictated by their sensitivity and total worth, the reactivity shim requirements, and certain criteria related to safe and efficient op- eration. These factors and a normal program of rod positions during an operating cycle are summarized briefly here. 9.1 General Considerations The drive mechanisms for the three rods are identical, and each rod has practically the same worth. Thus any one of the rods can be selected to be part of the servo control system which controls the reactor fission rate at power below 1 Mw or the core outlet temperature at higher powers. The other two rods are moved under manual control to shim the reactivity as required. The servo-controlled rod is called the regulating rod; the other two, shim rods. All rods are automatically inserted or dropped under certain conditions, so that all perform safety functions. (For a description of control and safety systems see Part II. Nuclear and Process Instrumentation. ) The criteria for the rod employment are as follows: 1. The reactivity is limited by fuel loading to the minimum required for full-power operation. Thus, at full power, with maximum poison and burnup, the rods are withdrawn to the limits of their operating ranges. 2. The maximum withdrawal of the shim rods ig set at 54 in. to avoid waste motion at the beginning of a rod drop. 3. The normal operating range of the regulating rod is limited by the reduced sensitivity at either end to between 15-in, and 45-in. with- drawal. (In this range the rod changes reactivity at 0.002 to 0.04% 3k/k per sec while being driven at 0.5 in./sec.) 4. Rod movements are programmed to minimize error in calculated rod worth due to interaction or shadowing effects. 97 5. While the core is being filled with fuel, the rods are withdrawn so that the reactor, when full, will be suberitical by about 1.0% 8k/k. This allows the source multiplication to be used to detect abnormalities, and provides reserve poison which can be inserted in an emergency. 6. Before the circulating pump is started, the rods are inserted far enough to prevent any cold slug from making the reactor critical. 9.2 ©Shim Requirements The reactivity changes due to various causes during an operating cycle depend, for the most part, on the type of fuel in the reactor. The amounts of rod poison which must be withdrawn to compensate for various effects are summarized in Table 9.1. Equilibrium samarium poisoning and the slow growth of other fission products and corrosion products are com- pensated by fuel additions rather than by rod withdrawal. The largest single item in Table 9,1, the xenon poisoning, depends on the flux, the stripper efficiency, the xenon diffusivity in the graph- ite, and the fuel-graphite xenon transfer. The tabulated values of xenon effect were calculated for a stripper efficiency of 50%, xenon diffusivity in the graphite of 1.5 x 107° ftz/hr, and a mass transfer coefficlent of 0.08 ft/hr. There is considerable uncertainty in these factors, and the Table 2.1. Rod Shim Requirements Effect (% 8k/k) Cause Tuel A Fuel B Fuel C Loss of delayed neutrons 0.3 0.3 0.3 Entrained gas 0.2 0.4 0.2 Power (0—10 Mw) 0.06 0.08 0.06 Xel3? (equilibrium at 10 Mw) 0.7 0.9 0.7 Samarium transient 0.1 0.1 0.1 Burnup (120 g of U?37) 0.03 0.07 0.03 e Total 1.4 1.9 1.4 98 xenon effect could be as little as one-third or as much asg twice the values tabulated. 9.3 Shutdown Margins When the rods are withdrawn to the limits set by criteria 2 and 3, the combined poison of the three rods is 0.5% 8k/k. The useful worth of the rods, from full insertion to the upper end of thelr operating ranges, is therefore less than the total worth (Table 4.1) by 0.5% 8k/k. The minimum shutdown margin provided by the rods is the difference between the useful worth of the rods and the shim requirements (Table 9.1)., (The shutdown margin will be greater than the minimum whenever any of the effects in Table 9.1 are present.) Minimum shutdown margins for fuels A, B, and C are 3.7, 5.2, and 3.8% ok/k, respectively. These mar- gins are equivalent to reductions in critical temperatures of 580, 530, and 550°F, respectively. If the 10-Mw equilibrium xenon poisoning were twice the values shown in Table 9.1, the minimum shutdown margins would correspond to critical temperature reductions of 470, 440, and 450°F, re- spectively. Thus criterion 6 is easily satisfied by fully inserting the rods before the pump is started. 9.4 Typical Sequence of Operations At the beginning of an operating cycle, when the core is being filled with fuel, the rods are positioned so that the reactor should be slightly subecritical when full. The rod poisoning which 1s necessary at this time depends on the total shim requirements and the current effects of samarium and burnup. (Xenon and other factors causing reactivity loss during op- eration will not normally be present during a fill.) Assuming that the shim requirements are as shown in Table 9.1 and that the fuel has peak samarium, no xenon, and no burnup during a fill, the rods would be posi- tioned to poison 2.8, 3.3, or 2.8% dk/k with fuels A, B, and C, respec- tively. This would leave 2.8, 4.3, or 2.9% dk/k in reserve, to be in- serted if abnormal conditions should require a rod scram, If the shim requirements are greater than shown in Table 9.1, the reserwve is accord- ingly less. During the fill all three rods will be at equal withdrawal. 99 This is to provide the best protection if only two of the three rods drop when called for. Before the pump is started, all three rods are fully inserted to give full protection against a cold slug making the reactor critical. {The rod position indicators can also be calibrated at this time.) After the pump is running, the shim rods are withdrawn to a prede- termined point, and then the reactor is made critical by slowly withdraw- ing the regulating rod. The amount of shim rod withdrawal is chosen to make the critical regulating rod position well below the position of the shim rods but within the range of adequate sensitivity. (The regulating rod and shim rod tips are kept separated to reduce the nonlinearities in worth which result from the regulating rod tip moving into and out of the shadow of the shim rods.) After the power is raised and more rod poison must be withdrawn, the shim rods are withdrawn together, if they are not already fully withdrawn, until they reach the maximum desirable withdrawal. The regulating rod is then allowed to work its way up, under control of the servo system, to shim for further reactivity changes. Table 2.2 summarizes rod positions and poisoning during the typical operating cycle with fuel C in the reactor. Table 9.2. Rod Positions During Typical Operation, Fuel C Rod Position Rod Poisoning Condition (in. withdrawn) (% 3k/k) Regulating Shims Regulating Shims Total Filling core (1% sub- 28.5 28.5 0.9 1.9 2.8 critical) Starting fuel pump 0 0 1.9 3.8 5.7 Going critical, no Xe, 28.4 54 1.2 0.1 1.3 peak Sm, no burnup At 10 Mw, no Xe, peak Sm, 29.4 54 1.1 0.1 1.2 no burnup At 10 Mw, equilibrium Xe 39.3 54 0.6 0.1 0.7 and Sm, no burnup At 10 Mw, equilibrium Xe 39.9 54 0.5 0.1 0.6 and Sm, 120 g of U233 burnup 100 10. NEUTRON SOURCES AND SUBCRITICAL OPERATION 10,1 Introduction When the reactor is subcritical, the fission rate and the neutron filux will depend on the neutron source due to various reactions and the multiplication of these source neutrons by fissions in the core. The fuel itself is an appreciable source of neutrons due to (a,n) reactions of alpha particles from the uranium with the fluorine and beryllium of the salt. There ig also a contribution from spontaneous fission. Thus the core will always contain a source whenever the fuel is present. After high-power operation the internal source will be much stronger, because of photoneutrons produced by the fresh fission products. For the initial startup, an external source can be used to increase the flux at the cham- bers used to monitor the approaxh to criticality. 10.2 Internal Neutron Sources 10.2.1 Spontaneous Figsion An absolutely reliable source of neutrons is the spontaneous fission of the uranium in the fuel. Uranium-238 is the most active, in this re- gard, of the uranium isotopes in the MSRE fuel. If fuel C, containing 0.8 mole % uranium of 35% enrichment, is used, the spontaneous fission source will be about 10°/neutrons sec. If highly (~93%) enriched uranium is used, the spontaneous fission source will be very small. Table 10.1 lists the specific emission rate of neutrons due to spontaneous fission 2 Also shown are the amounts of uranium in the core of' each isotope.3 (clean, critical loading) end the resulting total spontaneous fission neutron sources for the fuels whose compositions are given in Table 3.1. 10.2.2 Neutrons from (&,n) Reactions in the Fuel Alpha particles from uranium decay interact with some of the constit- uents of the fuel salt to produce a strong internal source of neutrons.-- All of the uranium isotopes are alpha-radicactive and any of the uranium alphas can interact with the fluorine and the beryliium in the fuel salt to produce neutrons. The more energetic of the alpha particles can also 101 Table 10,1. Neutron Source from Spontaneous Fissions in MSRE Core® . o Fuel A fuel B Fuel C Specific Emission Isotope Rate Mcb Source MCb source Mcb Source [n/(kgesec)] (kg) (n/sec) (keg) (n/sec) (kg) (n/sec) U234 6.1 0.3 2 0.2 1 0.2 1 yR35 0,51 27.0 14 16.5 8 26.4 13 236 5.1 0.3 2 0.2 1 0.2 1 U238 15,2 1.5 22 0.9 13 47,5 722 40 23 737 MEffective” core, containing 25 £t3 of fuel salt. b . ‘3 . Mass in core at clean, critical concentration. produce neutrons by interaction with lithium, but the yield is negligible in comparison with that from fluorine and beryllium, Table 10.2 summa- rizes the specific yields and gives the neutron source in the core for the clean, critical loading with different fuels. About 97% of the neu- trons are caused by alpha particles from U22%, Thus the (®,n) source is proportional to the amount of U234 present. 10.2.3 Photoneutrons from the Fuel Gamma rays with photon energies above 1.67 Mev can interact with the beryllium in the fuel salt to produce photoneutrons. This source is un- important before operation, when only the uranium decay gammas are present, but after operation at significant powers, the fission product decay gam- mas produce a strong, long-lived neutron source. Figures 10,1 and 10,2 show the rate of photoneutron production in the MSRE core after operation at 10 Mw for periods of 1 day, 1 week, and 1 month., The source is proportional to the power, and the source after periods of nonuniform power operation can be estimated by superposition of sources produced by equivalent blocks of steady-~-power operation. Table 10.2. Neutron Sources from (O,n) Reactions in MSRE Core” Fyy Alpha Fuel A Fuel B Fuel C Tsotope (Mev) [27?2:§?i9?] Yield Source Yield Source Yield Source & (n/10% @) (n/sec) (n/10% ) (n/sec) (n/10% a) (n/sec) ye34 477 1.64 x 1031 7.0 3.3 X 10° 7.8 2.3 x 10° 7.6 2.8 x 10° 4ea72 0.64 x 1012 6.6 1.2 X 10° 7.3 0.8 x 10° 7.1 1.0 x 10° U235 4,58 0.79 x 107 5.4 1.1 x 103 6.0 0.8 x 103 5.9 1.2 X 103 A 0.24 x 107 47 0.3 x 10° 5.3 0.2 x 103 5.2 0.3 x 103 lra 40 6.56 X 107 e 3 7.5 x 103 L8 5.2 x 103 7 8.1 x 10° v 20 0.32 x 107 3.2 0.3 x 103 3.7 0.2 x 103 3.6 0.3 x 103 U236 e 50 1.72 x 10° 49 2.4 x 103 5.5 1.7 X 103 5,4 2.1 x 103 o de5 0.63 x 107 45 0.8 x 102 5.1 0.6 x 103 5.0 0.7 x 103 y238 4.19 0.95 x 108 3.1 4 3.6 3 3.5 1.6 X 102 4a15 0.28 x 108 2.9 1 344 1 3.3 0.4 % 102 4o X 10° 3.2 X 105 3.9 X 107 Bprrective” core, containing 25 £13 of fuel salt of clean, critical concentration. <0t 103 UNCLASSIFIED ORNL DWG. 63.8171 10 10 SOURCE STRENGIH (neutrons/sec) L 8 12 16 20 phy 28 TIME AFTER SHUTDOWN (hr) Fig. 10.1. Photoneutron Source in MSRE Core After Various Periods at 10 Mw, 104 UNCLASS!FIED 9 ORNL DWG, 638172 SOURCE STRENGTH (neutrons/sec) 1 10 100 TIME AFTER SHUTDOWN (days) Fig. 10.2. Photoneutron Scurce in MSRE Core After Various Periods at 10 Mw. 105 The gamma-ray source used in the calculations is group IV of Blomeke and. Todd,34 which includes all gamma rays above 1.70 Mev. The probability of one of these gamma rays producing a photoneutron was approximated by the ratio of the Beg(y,n) cross section to the total cross section for gamma-ray interaction in a homogeneous mixture with the composition of the core. A Be?(y,n) microscopic cross section of 0.5 mb was used, and the total cross section was evaluated at 2 Mev. These assumptions lead to a conservatively low estimate of neutron source strength. 10.3 Provisions for External Neutron Source and Neutron Detectors 10.3.1 External Source For reasons which will be described later, it is desirable to supple- ment the inherent, internal source with a removable, extraneous source. Therefore, a thimble is provided inside the thermal shield on the opposite side of the reactor from the nuclear instrument shaft. The thimble is a 1-1/2-in. sched 40 pipe of type 304 stainless steel, extending vertically down to about 2 ft below the midplane of the core. It is mounted as close as possible to the inner surface of the shield for maximum effectiveness. 10.3.2 Neutron Detectors A nuclear instrument shaft is provided for all the permanently in- stalled neutron detecting instruments. This is a water-filled 3-ft-diam tube which slopes down to the inner surface of the thermal shield with separate, inner tubes for the various chambers. The shaft contains ten tubes, of which seven will be used for routine power operation (two wide- range servo-operated fission chambers, two compensated ion chambers, and three safety chambers). This leaves three tubes in which auxiliary or special~purpose chambers could be installed. Any chamber in the instru- ment shaft is in a sloping position, with the upper end farther from the core (and hence, in a lower flux) than the lower end. As a result, a long chamber in the instrument shaft is exposed to a lower average flux than a shorter one, 106 Two vertical thimbles, similar to the source thimble but made of Z- - in. sched 10 pipe, are installed in the thermal shield to accommodate tem- porary neutron detectors. The two detector thimbles are located 120 and 150° from the source thimble, one on either side of the permanent nuclear instrument shaft. The advantage of these vertical thimbles is that they place the entire length of a chamber close to the inner surface of the thermal shield, where it is exposed to a higher average neutron Ilux. 10.4 DNeutron Flux in Subcritical Reactor \ Changes in the reactivity of the subecritical reactor can be monitored if the fissions caused by the source neutrons produce a measurable neutron flux at the detectors mounted outside of the reactor vessel. The flux at a chamber depends on the source — its strength, the energy of the neu- trons, and, in the case of an extermal source, its location both with re- spect to the core and with respect to the chamber. The flux also depends on the amount of multiplication by fissions and the shape of the neutron fux distribution in the core, which is determined by the location of the source and the wvalue of k in the core. The count rate produced by a given chamber depends on the chamber sensitivity as well as on the neutron flux. Of interest in establishing the neutron-source requirements are the sensitivities of the chambers which will be used to observe the behavior of the reactor under subcrit- ical conditions, The fission chambers, which will be used to monitor routine approaches to critical (as well as power operation) are 6 in. long and have a counting efficiency of 0.026 count per neutron/cmz. In addition, BF3; chambers are available; they will be used during the initial critical experiments (and possibly to monitor routine reactor fills). These have a sensitive length of 26-1/4 in. and a counting efficiency of 14 counts per neutron/cm®. The steady-state flux in the core and thermal shield with a source in the thermal shield source tube was calculated?® Ffor two core condi- tions: the first, with no fuel in the core; the second, with the core filled with fuel salt containing 0,76 of the clean, critical uranium con- centration. In the latter case keff was calculated to be 0,91. Contri- ~ 107 butions from the internal neutron source were neglected. The calculated ratios of thermal neutron fluxes at the chambers to the source strength (n.eutrons/cm2 per source neutron) are given in Table 10.3. As a first approximation, the ratios of flux or count rate to source strength at keff above 0.9 can be assumed to change in proportion to the inverse of (1-%k ff) When the multiplication is high, that is, when (1 —k ) is quite eff small, most of the neutrons are produced by fissions in the core, with a spatial source distribution close to the fission distribution in a crit- ical reactor. The relation between the core power, or fission rate, in the critical core and the flux in the thermal shield was calculated in the course of the thermal shield design, using DSN, a multigroup, trans- port-theory code. For the case of a thick, water-filled thermal shileld, when the core power is 10 Mw, the predicted thermal neutron flux reaches a peak, 1 in. inside the water, of 1.2 X 101? neutrons cm™? sec™t, The ratio of peak flux to power is 1.2 X 10° neutrons cm™? sec™?t per watt, or 1.5 X 10°% neutrons em™? sec™! per neutron/sec produced in the core. It was estimated that a 6-in.-long chamber at maximum insertion in the instrument shaft would be exposed to an average flux of roughly 1 X 1077 Table 10,3, Fluxes Produced at Neutron Chambers by an External Source Average Flux/Source Strength Location ggzgzir {[H/(Cm .sec)]/(n/sec)} (in.) No Fuel E_.o = 0.91 X 1076 X 1076 120° thimble Any 13 18 150° thimble Any . 9 Instrument shaft (~180°) 6 2 26 0.6 1.7 108 2 sec™! per neutron/sec produced. For a 26-in.-long chamber, neutrons cm- the corresponding value is about 3 X 1078, A chamber in one of the ver- tical tubes Jjust inside the inner wall of the thermal shield would be ex- posed to an average Tlux of about 3 X 1077 neutrons cm~? sec™1 per neu- tron/sec produced in the core. With both an external and an internal source present, the flux at a particular location in the thermal shield can be roughly approximated by an expression of the form fexsex finsin ®=Db8, Tt T (10.1) The quantities Sex and Sin are the strengths of the external and internal sources, respectively. The factors fex and fin indicate the fraction of neutrons, produced in the core Ifrom the corresponding source neutrons, which reach the location in question. ©Since these factors depend on the flux shape, the values vary somewhat with ke The factor b is propor- tional to the fraction of the neutrons from ifie external source which reach the thermal shleld without first entering the core, that is, by scattering around the core. This factor 1s essentially independent of keff' The calculation of the flux distribution with an external source and no fuel in the core indicated that fex is essentially zero for this con- dition. Also, when there is no fuel in the reactor, Sin = 0. Thus, for this condition Eq. (10.1) reduces to ¢ = bS . (10.2) ex This expression permits direct evaluation of b for wvarious locations from the above calculation, When the reactor is near critical, the variation in fex and fin with k can be neglected to obtain approximate values for these quantities. The value of fin for various locations was cobtained from the critical flux distribution, and feX was Obtained from the distribution at keff = 0.91. The values obtained for the factors at the various proposed neutron chamber locations are listed in Table 10,4. These factors can be usged to 109 Table 10.4. Flux/Source Factors in MSRE Location Cham}"?i n%fingth (CE_Z ) (fglzg ) (iflllg ) X 1076 x 1077 x 1077 120° thimble Any 13 5 3 150° thimble Any 4 5 3 Instrument shaft 6 2 4 1 26 0.6 1 0.3 estimate the flux at the chambers for different source conditions either when the reactor is empty or when it is near critical (keff z 0.95). 10,5 Requirements for Source?3? A neutron source must perform several functions in the operation of a reactor, and each function places different requirements on the source. 10.5.1 Reactor Safety The most important function of a neutron source in the reactor has to do with reactor safety. If an adequate source is present, the statis- tical fluctuations in the level of the fission chain reaction will be negligibly small and the level will rise smoothly as the reactivity is increased to make the reactor critical. Furthermore, when the reactor becomes supercritical, the level will be high enough that temperature feedback becomes effective, and safety actions can be taken before enough excess reactivity can be added to cause a dangerous power excursion. As shown in Secs 12,2 and 12.7, the strength of the inherent (o-n) source is enough to satisfy the safety requirements for a source. This is convenient because the (@-n) source will always be present whenever there is any chance of criticality. This assurance of an adequate in- ternal source eliminates the usual safety requirement that an extraneous 110 source bhe installed and its presence proved by significant count rates on neutron chambers before a startup can begin. 10.5.2 Preliminary Experiments An extraneous source and sensitive neutron chambers are useful in the MSRE primarily because they comprise a means of monitoring the reac- tivity while the reactor is subecritical, or of following the nuclear power behavior at levels below the range of the ilonization chambers which pro- vide Iinformation at high power. For the initial critical experiment, it is desirable to have a sig- nificant neutron count rate before any fuel is added to the reactor. This guarantees that the condition of the reactor can be monitored at all times during the experiment. Table 10,5 lists the external source strength re- quired to produce a count rate of 2 counts/sec on the wvariousg chambers with no fuel in the reactor. 10,5.3 Routine Operation After the preliminary experiments, only the chambers in the nuclear instrument shaft will be available to monitor the reactor flux. The function of the neutron source in routine operation is to permit monitoring the flux during reactor startups so that the operation is or- derly. A normal startup of the MSRE involves two separate steps: (1) filling the reactor with fuel salt and (2) withdrawing the control rods Table 10.5. External Source Required for 2 Counts/sec with No Fuel in Reactor source . Chamber Counting Efficiency St th Location Type {(counts/sec)/[n/(cm?esec)]} (n?i?%) 120° thimble BF5 14 1 x 104 150° thimble BF; 14 4 X 10% Instrument shaft Fission 0.026 4 x 107 BF3 14 2 x 10° 111 to make the reactor critical. Although the first operation will normally leave the reactor subcritical, it is desirable to monitor the flux during this step to ensure that no abnormal conditions exist. This requires that a significant count rate exist before the fill is started, and the source requirements are the same as for the initial critical experiment. The second phase of the startup involves changing the multiplication constant from about 0.95 (the shutdown margin attainable with the control rods) to 1,0, This operation should, if possible, be monitored by instruments which are still useful after criticality is attained; in the MSRE, these instruments are the servo-operated fission chambers. A source of 8 X 108 neutrons/sec is required to produce a count rate of 2 counts/sec on a fully inserted fission chamber when k = 0,95, 10,6 Choice of Extermal Source The source requirements of the MSRE can be met in a number of ways. One of the most desirable sources from the standpoint of cost and ease of handling is the Sb~Be type, and such a source that meets the calculated requirements can be easily obtained. However, Sbl?4 nas only a 60-day half-life, so the initial intensity of such a source must be substantially greater if frequent replacement is to be avoided. The calculated require- ments can also be met with a Pu-Be source. Such a source would be more expensive, and there is a containment problem because of the plutonium content. On the other hand, the long half-life of plutonium would elimi- nate the problems associated with source decay. Becauge the flux calculations are subject to substantial errors, the final specification of the source will be based on measurements to be made shortly after the reactor vessel containing the core graphite is in- stalled inside the thermal shield. (The construction and startup schedule is such that there is time for procurement of a source after these meas- urements and before the source is needed for nuclear operation.) 112 11. KINETICS OF NORMAL OPERATION Studies of the kinetic behavior of the reactor fall into two cate- gories. One deals with the behavior in normal operation, when the re- actor is subjected only to moderate changes in load demand and to small, random disturbances or "noise.” The concern here is with stability — absolute and relative. (Absolute stability means that a disturbance does not lead to divergent oscillatlions; relative stability refeers to the magnitude and number of oscillations which occur before a transient dies out.) The other category of kinetics studies treats the response of the system to large or rapid changes in reactivity such as might occur in abnormal incidents. Studies of the first kind are covered in this chapter. The next chapter deals with safety studies, or kinetics under abnormal conditions. 11.1 Very Low Power When the MSRE is operated at very low power, with the temperature held constant by the external heaters, the fission chain reaction is controlled by the control rods alone. The kinetic behavior of the fission rate under this condition is determined by the prompt neutron lifetime and the effective delayed neutron fractions and is not unusual in any way. The neutron lifetime is between 2 and 4 X 104 sec, depending on the fuel salt composition. (For comparison, the lifetime in mosit water-moderated reactors is between 0.2 and 0.6 x 10™* sec, and large, graphite-moderated reactors have lifetimes of about 10 X 10™4 sec. ) Although the effective delayed neutron fractions are considerably lower than in a fixed-fuel reactor using U235, this presents no important problem of control. 11.2 Self-Regulation at Higher Power When the reactor power is high enough to have an appreciable effect on fuel and graphite temperatures, the power becomes self-regulating. That is, because of the negative temperature coefficients of reactivity, 113 the nuclear power tends to follow the heat extraction, or load, with- out external control by the rods. The kinetic behavior under these conditions is governed by the fuel and graphite temperature coefficients of reactivity, power density, heat capacity, heat transfer coefficients, and transport lags in the fuel and coolant circuits. 11.2.1 Coupling of Fuel and Graphite Temperatures One characteristic of the MSRE which profoundly influences the self-regulation is the rather loose coupling between the fuel and the graphite temperatures. This 1s caused by a low ratio of heat transfer to thermal inertia and a disproportion of heat generation between the fuel and graphite. Heat transfer between the graphite and fuel is about 0.020 Mw per °F of temperature difference. The total heat capacity of the graphite is 3.7 Mw-sec per °F of temperature change. The ratio of heat transfer to graphite heat capacity is only about 0.005°F/sec per °F. This means that with a temperature difference of 100°F between the fuel and the graphite, the heat transferred is only enough to raise the graphlte tem- perature at 0.5°F/sec. The heat capacity of the fuel in the core is 1.7 Mw-sec/°F, less than half that of the graphite. But 93% of the fission heat is generated in the fuel; only 7% in the graphite. Thus, the core fuel temperature tends to change much more rapidly than that of the graphite whenever there is an imbalance between the heat generation and the heat removal from the core. Such imbalances would occur, for example, in any power excursion or undershoot, or whenever the fuel inlet temperature changes. The difference in the time responses of the fuel and graphite tem- peratures makes it necessary to treat them separately in any analysis of the MSRE kinetics. 11.2.2 Transport Lags and Thermal Inertia The kinetic behavior of the reactor is determined not only by the core characteristics but also by the characteristics of the entire heat- removal system, which includes the radiator, the coolant salt loop, the fuel-coolant heat exchanger, and the fuel circulating loop. 114 The coolant loop contains 44 ft? of salt, with a total heat ca- pacity of 2.9 Mw—sec/°F. At an 850-gpm circulation rate, the loop cir- cuit time is 23 sec. There is 67 £t of fuel salt in circulation, having a total heat capacity of 4.6 Mw-sec/°F. The fuel circulation rate is 1200 gpm, giving a circuit time of 25 sec. There is also additional thermal inertia due to the metal of the piping and heat exchanger. Because the circuit times are rather long and the heat capacities are large compared with the normal operating power, the system response to changes in heat removal at the radiator is rather slow. 11.2.3. Simulator Studies The kinetics and stability of normal operation were studied by a detailed simulation of the entire reactor system with an analog computer. By this method it was feasible to include the many effects of fluid mixing, loop transit times, heat capacities, heat transfer-4AT relations, temperature coefficients of reactivity for the fuel and graphite, and the reactivity-power relations. Studies of operation at power without external contrcl of the re- activity were carried cut with two different analog representations of the reactor. In the first model, the core was represented as a single major region comprised of two subregions of fuel and one subregion of graphite., Figure 1l1l.1l is a schematic diagram which shows the treatment of the thermal effects in the fuel and graphite in this model. In the second model, the core was subdivided into nine major regions, as shown in Fig. 11.2. Thermal effects were treated separately for each major region by the same relations used for the single major region in the first model of the core. The purpose of the subdivision of the core was to better approximate some of the effects of spatial variation of the power gener- ation, fuel and graphite temperatures, and the nuclear importance in the actual core. Temperaturegs in each of the nine regions were weighted to ob- tain the averages which determine the net effect on reactivity. Figures 11.3 and 1l.4 show the response of the system with the nine- region core model to changes in simulated power demand in the absence of external control action. In both cases the demand was changed by changing 115 UNCLASSIFIED ORNL—-DOWG 63-7318 GRAPHITE -7 _\.._,-,-a—- FUEL-GRAPHITE /4-’“;’/’ \ HEAT TRANSFER — FUEL FUEL L = (Tehin——_ Te/ - Tio | = (7T¢lour = 7f2 7r = Try — 7 “— / — ! T PERFECTLY MIXED SUBREGIONS Fig. 11.1. Analog Model of Reactor-Core Region. Nuclear power is produced in all three subregions. UNCLASSIFIED ORNL-DWG 63-7319 (7¢douT ¢ ! *—“ D ~ — - ——t— | FLow (7¢) 1N Fig. 11.2. Schematic Breakdown of 9-Region Analog Model. 1240 1220 1200 1180 TEMPFRATURE (°F) 1160 1140 12 10 FILUX POWER (Mw) Fig. 11.3, Power Demand. 116 UNCLASSIFIED ORNL DWG, 63-8228 200 400 00 800 1000 TIME (sec) Response of 9~Region Model of MSRE to an Increase in 117 UNCLASSIFIED ORNL DWG. 63-8173 1280 1240 TEMPERATURE (°F) 1200 1160 10 FLUX POWER (Mw) O 0 100 200 300 400 500 600 700 800 900 TIME (sec) Fig. 11.4. Response of 9-Region Model of MSRE to a Decrease in Power Demand. 118 the simulated air flow through the radiator, the ultimate heat sink in the reactor system. For the power increase in Fig. 11.3, the simulated air flow was raised from 3% to 100% of the design value at O.5%/sec. As shown, there was a moderate power overshoot and about 15 min was required for the power and the fuel temperatures to approach steady-state values. The response to & decrease in alr flow to 8% of the design value at 3%/sec is shown in Fig. 1l.4. In this simulator test, the temperature of the graphite in an important region of the core (region 3 in Fig. 11.2) was recorded. Besides showing the transient response of the reactor system, Fig. 11.4 illustrates the shift in steady-state temperatures at different powers which results if there 1s no adjustment of the control rods. This shift comes about because the heat generated in the graphlite must be transferred to the fuel for removal from the core, causing the fuel and graphite temperatures to diverge. Since the temperature coefficients of reactivity of both the fuel and the graphite are negative, the tendency of the graphite temperature to rise at higher powers forces the fuel tem~ perature to decrease to keep the net reactivity change zero. Figures 11.5 and 11.6 show the response of the simulated nuclear power in the one-regiorn core model to changes in power demand similar to those used to produce Figs. 11.3 and 1ll.4. It may be noted that the simulation involving the simpler core model shows a significantly greater tendency toward sustained power oscillation at low powers. The reason for the different results i1s not clear. The reactor system models differed in several respects beside the core, and, because the calculations were done at different stages of the reactor design, they used somewhat different values for the current reactor design data. Despite the differences in the simulator results, an important con- clusion can be drawn from them. That is: although the negative tempera- ture coefficients of reactivity make the reactor capable of stable self- regulation, an external control system is desirable because the reactor is loosely coupled and sluggish, particularly at low power. (Neither of the models included compressibility effects due to entrained gas, but inclusion of these effects would probably not change the conclusion. ) UNCLASSIFIED ORNL DWG. 638174 10 FLUX POWER (Mw) 200 Loo 600 800 1000 1200 1400 1600 TIME (gec) Pig. 11.5. Response of 1-Region Model of MSRE to an Increase in Power Demand. 61T UNCLASSIFIED ORNL DWG. 638175 (#90) SEMO4 XNTd 1800 1600 1400 1200 1000 800 600 Loo 200 TIME (sec) Response of 1-Region Model of MSRE to a Decrease in Fig. 1l.6. Power Demand. 121 11.3 Operation with Servo Control In order to eliminate possible oscillations and to obtain the de- sired steady-state temperature-power relations, a servo control system was designed for use in operation at powers above 1 Mw. One control rod is used as part of a servomechanism which regulates the nuclear power as required to keep the fuel temperature at the reactor vessel outlet within narrow limits. Simulator tests showed that the servo control system was capable of holding the fuel outlet temperature practically constant during load changes betwee 1 and 10 Mw in times of the order of 5 to 10 min with- out significant overshoot of the nuclear power. At powers below 1 Mw, the servo control is switched to control the flux, or nuclear power, at a set point, and the temperature is controlled by manual adjustment of the radiator heat removal. Adjustment of the ex- ternal heaters may alsc be used at times. The design and performance of the servo control system are described in detail in Part II. Nuclear and Process Instrumentation. 122 12. KINETICS IN ABNORMAL SITUATIONS — SAFETY CALCULATIONS 12.1 Introduction There are several concelvable incidents which could result in re- activity increases larger or faster than those encountered in normal operation of the reactor. Iach of these incidents rmust be examined from the standpoint of reactor safety, to determine whether there is a possi- bility of damage to the reactor or hazard to personnel., Because the concern is safety, a conservative approach must be used. If the analysis of an incident indicates that the consequences may be intolerable, then protection must be provided to guard against damage and ensure the safety of reactor operation. (Control and safety systems are described in Part II. iuclear and Process Instrumentation.) 12.2 General Considerations The most likely form of damage from excessive reactivity additions in the MSRE is breach of the control rod thimbles in the core by a com- binetion of high fuel temperature and the high pressure produced in the core by the rapid thermal expansion of the fuel. The severity of the power, temperature, and pressure transients associated with a given reactivity incident depends upon the amount of excess reactlivity involved, the rate at which it can be added, the ini- tial power level, the effectiveness of the inherent shutdown mechanisms, ancd the efficacy of the reactor safety system. All of these factors de- bend to some extent on the fuel composition, because this determines the magnitude of the various reactivity coefficients and the control rod worth (see Tables 3.5 and 4.1). In general, equivalent physical situations lead to larger amounts of reactivity and greater rates of addition with fuel B than with either A or C. This is a consequence of the larger values of the reactivity coefficients and control rod worth, the absence of the poisoning effect of thorium or U?38) and the lower inventory of U??® in the core. 123 The power and temperature transients associated with a given re- activity incident increase in severity as the initial power level is reduced. The reason for this is that, when the reactor becomes critical at very low power, the power must increase through several orders of magnitude before the reactivity feedback from increasing system tempera- tures becomes effective. Thus, even slow reactivity ramps can introduce substantial excess reactivity if the reactor power is very low when Kepr = 1 The power level in the MSRE when the reactor is just critical de- pends on the strength of the neutron source, the shutdown margin prior to the approach to criticality, and the rate at which reactivity is added to make the reactor critical. The minimum neutron source strength which must be considered is 4 x 10° neutrons/sec, which is the rate of production in the core by (G-n) reactions in the fuel salt. Ordinarily the effective source will be much stronger, because an external Sb-Be source will normally be used to supply about 107 neutrons/sec to the core and, after the reactor has operated at high power, fission product gamma rays will generate up to 1010 photoneutrons/sec in the core. The ratio of the nuclear power at criticality to the source strength varies only #10% for reactivity addition rates between 0.05 and 0.1% 8k/k per second and for the maximum shutdown margins attainable in the MSRE. For these conditions, the power level at criticality is about 2 mw if only the inherent (Q-n) source is present, and is proportionately higher with stronger sources. The power level at criticality increases for lower rates of reactivity addition. The principal factor in the inherent shutdown mechanism for the MSRE is the negative temperature coefficient of reactivity of the fuel salt. Since most of the fission heat is produced directly in the fuel, there is no delay between a power excursion and the action of this coefficient. The graphite moderator also has a negative temperature coefficient of re- activity; but this temperature rises slowly during a rapid power tran- sient, because only a small fraction of the energy of fission is absorbed in the graphite. As a result, the action of the graphite temperature coefficient is delayed by the time required for heat transfer from the fuel to the graphite. Since fuel B has the largest negative temperature 124 coefficient of reactivity, a given reactivity incident produces smaller excursions with this fuel than with either of the other two. The MSRE safety system causes the three control rods to drop by gravity when the nuclear power reaches 15 Mw or when the reactor outlet temperature reaches 1300°F. In the anslysis of reactivity incidents, conservative values were assumed for delay time and rod acceleration, namely, O.1 sec and 5 ft/sec2, respectively. It was also assumed that one of the three rods failed to drop when called for. 12.2 Incidents Leading to Reactivity Addition In the MSRE the conceivable incidents which could result in signifi- cant additions of reactivity include the following: . uncontrolled rod withdrawal, cold-slug accident, abnormal concentration of uranium during fuel additions, displacement of graphite by fuel salt, . premature criticality while the core is being filled, oo o~ W . fuel pump powér failure. Estimates of the maximum addition rates and total reactivity as- sociated with the first four incidents, together with the initial con- ditions postulated, are summarized in Table 12.1. Brief descriptions of these postulated incidents and the bases for the rates listed in Table 12.1 are as follows. 1. Simultaneocus, continuous withdrawal of all three rods is ini- tiated, starting with the reactor critical at 1200°F and the rod tips near the position of maximum differential worth. The rod withdrawal speed is 0.5 in./sec and the maximum differential worth was obtained from Fig. 4.2. 2. The cold-slug accident occurs when the mean temperature of the core salt decreases rapidly because of the injection of fluid at ab- normally low temperature. Such an accident would be created by starting the fuel circulating pump at a time when fuel external to the core has been cooled well below that in the core, if such a situation were pos- sible. A detailed study was made for a case in which fuel at 900°F is Table 12.1. Maximum Expected Reactivity Additions in Postulated Operating Incidents Maximum Estimated Incident Description Reactivity Rate [ (% 8k/k)/sec] Maximum Total Reactivity (%) Initial Power Level Assumed in Accident (w) 1 Uncontrolled withdrawal of 3 rods 0.10 2 Cold-slug accident® 0.16 3 Abnormal concentration of uranium 0.12 during fuel addition at pump bowl 4 Graphite stringer breakage 0.02 l.5 C.37 0.22 0.002° 1000 0,01 .01 “Determined by maximum operating excess reactivity (~d%) . bPower at keff = 1 for minimum neutron source. ©900°F fuel salt pumped. into core, which is initially critical at 1200°F. Gt 126 pumped at 1200 gpm into the core, which is initially critical at a uni- form temperature of 1200°F. The maximum reactivity addition rate in this case depends on heat transfer between salt and graphite and transient nu- clear heating before the core is filled. The product of the salt temper- ature reactivity coefficient and the temperature decrease (300°F) divided by the core fluid residence time gives the rough estimate of reactivity addition rate listed in Table 12.1. 3. A maximum of 120 g of highly enriched uranium can be added as frozen salt at the pump bowl. An upper limit on the transient caused by a bateh going into circulation was found by assuming that the fresh salt failed to mix gradually and passed through the core as a "front" of highly concentrated uranium. The rate listed in Table 12.1 is the meximum rate of addition, accounting for the change in nuclear importance as the con- centrated salt moves upward through the channels. The total reactivity added would increase to a maximum when the uranium is near the center of the core, then decrease as the fuel exits. 4. Replacement of graphite by fuel produces a reactivity increase. Breakage of a graphite stringer into two pieces while fuel is circulating through the core could allow the upper section to float upward and fuel salt to move into the space about the fracture, were it not for the re- straining rods and wires through the lower and upper ends of the stringers. An upper limit of the potential reactivity increase due to loss of graph- ite was calculated by assuming that the entire central graphite stringer was replaced by fuel salt. The total reactivity, listed in Table 12.1, is small, compared with that in the other incidents, and requires a time approximately equal to the core residence time for its addition. Incidents 5 and 6 are not included in Table 1lZ2.1l, since the condi- tions important to these incidents cammot be simply characterized by a reactivity addition rate. In brief, the filling accident is postulated to occur as follows: When the reactor is shut down, the fuel salt is drained from the core. During the subsequent startup, the fuel salt and graphite are preheated and the control rods are positioned so that the reactor remains sub- critical while filling. Criticality with the core only partially filled 127 could result, however, if the core or salt temperature were abnormally low, the fuel salt were abnormally concentrated in uranium, or the con- trol rods were fully withdrawn. In the case of the fuel pump power failure, there is an increase in reactivity because delayed neutron precursors are no longer swept out of the core when the pump stops. More important, from the standpoint of rising temperatures, is the sudden decrease in heat removal from the core, From the reactivity additions listed in Table 12.1, it 1s apparent that of the four incidents listed, the rod withdrawal and the cold-slug accident are potentially the most serious. The analysis of these inci- dents and of the filling accident and the pump stoppage are described in the sections which follow. 12.4 Methods of Analysis The general method used to estimate the consequences of the various incidents was numerical integration, by means of a digital computer, of the differential equations describing the nuclear, thermal, and pressure behavior of the reactor. In the development of the methods of analysis, realistic rather than pessimistic approximations were made wherever pos- sible. The conservatism necessary in an appraisal of safety was then introduced by the choice of the initial conditions for the postulated incidents. The mathematical procedures developed for the analysis of the MSRE kinetics are described in this section. Symbols used in this description are defined in Sec 12.4.4. 12.4.1 Reactivity-Power Relations The time dependence of the nuclear power was described by the well- known relation N P+ _fl AT (12.1) i=1 _k(1-8)-1 P Z 128 Six groups of neutrons were included in the summation. The effec- tive number of precursors (actually, the latent power agsociated with their decay was represented by the equation for fixed-fuel or noncircu- lating reactors: r, = - NI (12.2) An allowance was made for the effects of circulation on the contribution of delayed neutrons by using reduced values of Bi (see Chap. 6). The effective multiplication constant, k, was represented by the sum of several terms: k=1 4k - (TF-T0) ~ ocg(Tg ~ Tgo) . (12.3) Here kex is the reactivity added by all means other than changes in the fuel and graphite temperatures. Temperature effects are represented by the last two terms in (12.3): Q%(T? — T?O) is the reactivity effect of changes in fuel temperature, which responds rapidly to power changes, and Qé(Tg ~— Tgo) is the effect of the graphite temperature, which responds more slowly. The equations gilven above are intrinsically space-independent ap- proximations in which the response of the reactor is characterized by the time behavior of the total power, a single temperature for the fuel and another for the graphite, and the two parameters G% and aé. In order to complete the mathematical description of the reactor kinetics, the fuel and graphite temperature distributions must be reduced to a single charac- teristic temperature for each, which are related to the heat generation rate, P. The relations must necessarily involve heat removal from the core, heat capacities of the fuel and the graphite, and heat transfer between fuel and graphite. 12.4.2 Power-Temperature Relations Two different models were used to approximate the exact thermal relations in the core. ot 129 The first power-temperature model assumed that the effective average temperature in the core was simply a weighted average of the inlet and outlet fuel temperatures: * T, = OT o + (1 - Q)Tfi . (12.4) It was also assumed that the nuclear average temperatures for the fuel and graphite were identical with the bulk average temperatures, which are governed by 8,Tp = 1-9y)P- WCP(TfO - Tfi) + h(Tg — T £ (12.5) o) Séfig = yP — h(fig-m'fif) . (12.6) These approximations were combined with the neutron kinetics equations in an IBM 7090 program called MURGATROYD.>® In the second model, an approximate calculation was made of the time dependence of the spatial temperature distributions of the fuel and graph- ite. These temperature distributions were then weighted with respect to nuclear importance in order to obtailn single nuclear average temperatures for the fuel and graphite. The average temperatures then determined the reactivity feedback. In calculating the temperature profiles, the shape of the core power distribution was assumed to be time-independent; how- ever, the magnitude of the total power varied in accordance with Eq. (12.1). The temperature distributions as a function of time were calculated by replacing the macroscopic heat balance Egs. (12.5) and (12.6) by "local" heat balances on salt and graphite in the individual channels: an an . 0 h(Tg-— Tf) US TSt 5. T T eoc. (12.7) Pr-ep Py oT & h{(T —~ T g___ g _ ( g f) (12.8) ot o C a p C ’ g g g8 ¢ 130 T = T(r,z,t), ¢ = o(r,z,t) . Note that the fluid temperature equation is now a partial differential equation, because of the presence of the transport term u(BTf/Bz). The shape of the axial power distribution was assumed to be sinuscidal: L - F P(t . ®f(r,z,t) = ( 7)Vf(r) (t) 3-81n-%?-, (12.9) @g(r,z,t) =.Z_Eifgrfflgil€§.sin.%§-. (12.10) g With the above approximations, it was possible to reauce the procedure of solving (12.7) and (12.8) to numerical integrations over only the time variable. The temperature at any point along the channel depends on the temperature distribution along the channel at the time the fuel enters the channel and the subsequent power-time history. The power-time re- lation was again obtained by integrating Eqs. (12.1) and (12.2). How- ever, the temperature feedback terms are now based on nuclear average temperatures, in which the fuel and graphite temperature profiles at time t are weighted with respect to nuclear importance [see Eq. (3.2) for the general definition of the nuclear average temperature]. Using the sinusoidal approximation for the axial variation of the importance func- tion and I(r) to represent the radial variation of the importance: R H — ine L2 . J; J; [Tj(r,z,t) Tfi] I(r) sin T odr dz Tj(t) - Tgy = , (12.11) R H jfl jfi 1(r) sin? 22 r dr dz /0 Y0 H Jg=1T, 8 . With the further assumption that heat conduction effects are small com- pared with the heat generation terms, the radial dependence of the tem- perature rise is proportional to the radial power density, so that (12.11) may be further simplified: 131 H _ ip2 22 . . J; [Tj(z,t) Tfi] sin® — dz Tj(t) - Tpy = Fp 7 , (12.12) Jfl sin2¥55 dz 0 H J=1%, g, where R J; F(r) I(r) r ar F; = . (12.13) R J; I(r) r ar The procedure for solution of the kinetics equations thus consists of calculating the temperature profiles from Egs. (12.7) and (12.8), the nuclear average temperature from Eq. (12.12), and the power-time behavior from Egs. (12.1), (12.2), and (12.3). An IBM 7090 program, ZORCH, was designed to obtain the solution of this set of equations by numerical approximation methods .37 12.4.3 Temperature-Pressure Relations During any excursion in the fuel temperature, the pressure in the core will rise and fall as the fuel expands and contracts. These changes result from the inertial effect of acceleration of the fuel salt in the reactor outlet pipe leading to the pump bowl, changes in friction losses in the pipe, and the compression of the gas space in the pump bowl. If the fluid is assumed to be incompressible, so that there is no effect of pressure on reactivity, the hydrodynamics equations can be solved in- dependently of the power-temperature equations. A simplified model of the primary salt system, similar to that utilized by Kasten and others for kinetics studies relating to the Homogeneous Reactor Test,38 was used for approximate calculations of the pressure rise. It is assumed that the fluid density can be adequately approximated by a linear de- pendence on the temperature: 132 o(T.) = ¢° +§§— (T, — T2) , (12.14) T where Tf is the bulk average temperature of the salt in the reactor core. The other basic relations required for calculation of the pressure rise are the force balance on the fluid in the outlet pipe and the equation of continuity for the core salt: M - - - 2 Toe, U = A(pc P, fUu<) , (12.15) . A p=—-V—pO(U—UO) . (12.16) f The compression of the gas in the pump bowl is assumed to be adiabatic: vE = pO (vt 12.17 Py Vp = Pplp) ( ) The resulting equation for the pressure rise is36 p_ - p0 = C1l% + Coy + Ca¥ (1 + Caf)] (12.18) In this expression x and y are the dimensionless power and the dimension- less fluid temperature, defined as x = P/F° , (12.19) 8p(Tp = Tp ) = =S5 . and the constants are defined as Ve 1 9p M(1 — )PP ClL=—"" <5 o=, (12.21) A p° OT, ld4g AS, . (nA) 144g A = — 0w . Cz Py VoM ’ (12.22) 133 l44gCA Cy = 2Ug-——35——-, (12.23) V(1 - 7)F 3p 2AU°%8 0" 5T f The first term on the right hand side of {12.18) arises from acceleration of fluid in the outlet pipe, the second results from the compression of the pump bowl gas, and the last represents the pressure drop due to friction loss in the pipe. This equation is the basic approximation for the transient core pressure rise utilized in the kinetics programs ZORCH and MURGATROYD. 12.4.4 Nomenclature for Kinetics Eguations A Cross-sectional area of outlet pipe ap Cross-sectional area of fuel channel ag Cross-sectional area of graphite stringer Ci Constant defined by Eq. 12.21 Co Constant defined by Eq. 12.22 Ca Constant defined by Eq. 12.23 Cy Constant defined by Eq. 12.24 £ Friction loss in outlet pipe F Radial distribution of power density F; Importance-weighted average of F g, Dimensional constant,(ft*lbmass)/(secz-lbfgrce) H Height of core h Heat transfer factor, graphite to fuel I Radial distribution of nuclear importance k Multiplication factor kex Reactivity added by external means £ Neutron lifetime M Mass of fuel in outlet pipe to pump N Number of delayed neutron groups n Ratio of gpecific heats 134 Power Pressure in core b kg W 0 g Pressure in pump howl Hd Radius of core Radial distance from core center line Total heat capacity of fuel in core Total heat capacity of graphite Local temperature of fuel H &Jd m n H H R M Local temperature of graphite H Nuclear average temperature of fuel 3 Nuclear average temperature of graphite H ] ok Hhk 07 H Bulk average temperature of fuel H| Bulk average temperature of graphite o Fuel inlet temperature H [ Fuel outlet temperature H o Time Velocity of fuel in a channel Velocity of fuel in outlet pipe < O £ o H o3 Hy Volume of fuel in core <3 Volume of graphite in core o Volume of gas in pump &S Heat capacity of fuel flow 3 Normalized power Normalized fuel temperature Axial distance from bottom of core Q N <9 N H Fuel temperature coefficient of reactivity Graphite temperature coefficient of reactivity Fraction of neutrons in delayed group i Total fraction of delayed neutrons Fraction of heat produced in graphite Latent power associated with delay group i . Temperature weighting factor Decegy constant for group 1 T Y O MR T o Q e e R Density © Q Volumetric heat capacity ¢ Power density Superscript O refers to initial conditions 135 12.5 MSRE Characteristics Used in Kinetics Analysis Table 12.2 summarizes the properties of the MSRE which affect the kinetics and gives the values which were used in the last analysis. Table 12.2. MSRE Characteristics Affecting Kinetic Behavior Fuel Salt A B C Prompt neutron lifetime (sec) 2.29 x 10~% Temperature coefficients of reactivity [(8k/k)/°F] Fuel —3.03 x 10™° Graphite —3.36 X 1077 Fuel density (1b/ft3) 144 Delayed neutron fraction Static Circulating Residence times (sec) Core External to core Fraction of heat generation In fuel In graphite Core heat capacity [(Mw-sec)/°F] Fuel Graphite Graphite-to-fuel heat transfer (Mw/°F) Core fuel volume (ft3) Fuel volumetric expansion co- efficient (°F 1) Length of line to pump bowl (ft) Cross sectional area of line (ft?) Friction loss in line [psi/(ft/sec)?] Pumb bowl initial pressure (psig) Volume of gas in pump bowl (ft3) Ratio of specific heats of helium (c_/c_) v 3.47 X 10-4 2.40 x 10°% 97 x 107° 3,28 x 10°° 91 X 10°° —3.68 x 10™? 134 143 o —4’l 0.006e7 0.0036 9.37 16.45 0.933 0.067 1.74 3.67 0,020 25.0 1.18 x 1074 16.0 0.139 0.020 5 2.5 1.67 136 1l2.6 Preliminary Studies 12.6.1 Early Analysis of Reactivity Incidents>® An early study was made in which each of the accidents described in Sec 12.3 was analyzed, using the space~independent kinetics program MURGATROYD to calculate power, temperature, and pressure excursions. Some calculations of the response of the reactor to arbitrary step and ramp additions of reactivity were also made, in order to better define the limits which would lead to internal damage to the core. The nuclear characteristics used in this study were similar to those listed in Table 12.2 for fuel A. The results of the preliminary study indicated that none of the accidents analyzed could lead to catastrophic failure of the reactor. The extreme cases of cold-slug accidents, filling accidents, and uncon- trolled rod withdrawal led to predicted core temperatures high enough to threaten internal damage. Because each of these accidents could happen only by compound fallure of protective devices, and because 1in each case there existed means of corrective action independent of the primary pro- tection, damage was considered to be very unlikely in the cases considered. The calculated response to arbitrary step and ramp additions of re- activity indicated that damaging pressures could occur only if the addi- tion were the equivalent of a step of about 1% 5k/k or greater, well beyond the severity of foreseeable accldents. 12.6.2 Comparison of MURGATROYD and ZORCH Results After the digital program ZORCH became available, some kinetics calculations were made to compare the excursions predicted by this method with those computed with MURGATROYD. As expected, differences were found in the calculated power, temperature, and pressure excursions obtained from the two kinetics programs. The differences arise because the ap- proximations used in MURGATROYD for the nuclear average temperature and the rate of heat removal from the reactor are poor during a rapid power transient, whereas these quantities are treated much more realistically in ZORCH. 137 An example of the differences in MURGATROYD and ZORCH results is illustrated in Fig. 12.1, where the power and-temperature transients following a prompt-critical step in reactivity are compared. Because ZORCH computes a spatial temperature distribution and gives the greatest welght to the most rapidly rising temperatures, its nuclear average tem- rerature rises more rapidly than the fuel bulk average temperature or the temperature computed by MURCATROYD. The power excursion is therefore cut off at a lower peak than that calculated by MURGATROYD. The inte- grated power is also less in the ZORCH results, causing a smaller rise in the mixed-mean temperature of the fuel leaving the core (TO in Fig. 12.1). The highest temperature in Fig. 12.1, (To)max’ is the temperature Predicted by ZORCH for the outlet of the hottest fuel channel. This fuel would mix in the upper head of the reactor vessel with cooler fuel from other channels before reaching the ocutlet pipe. 12.7 Results of Reactivity Accident Analyses The results of the most recent analyses of the important reactivity accidents are described in this section. 12.7.1 Uncontrolled Rod Withdrawal Accident This accident is most severe when criticality is achieved with all three control rods moving in unison at the position of maximum differen- tial worth. Since this condition is within the range of combinations of shutdown margin and rod worth for all three fuels, it was used as a basis for analyzing this accident. The maximum rates of reactivity addition by control-rod withdrawal are 0,08, 0,10, and 0.08% 8k/k per second when the system contains fuels A, B, and C, respectively. The initial transients agssociated with these ramps were calculated for_fuels B and C starting with the reactor Jjust critical at 0.002 w and 1200°F. (The transients for fuel A would be practically the same as for fuel C.) The first 15 sec of the transients in some of the variables are shown in Figs. 12.2 and 1l2.3 for fuels B afid C respectively. The curves illustrate the behavior of the power, the fuel and graphite nuclear aver- ¥ age temperatures, Tf and Tg, the temperature of the fuel leaving the 138 UNCLASSIFIED ORNL DWG. 63-8229 1600 1500 1400 TEMPERATURE (°F) 1300 1200 120 100 POWER (Mw) 40 0 1 2 3 4 5 6 T 8 9 10 TIME (sec) Fig. 12.1. Power and Temperature Transients Following a Prompt Critical Step in Reactivity; Fuel A; Comparison of ZORCH and MURGATROYD Kinetics Models. 139 UNCLASSIFIED ORNL DWG. 63.8176 TEMPERATURE (°F) POWER (Mw) c 2 L & 8 10 12 14 16 TIME (sec) Fig. 12.2. Power and Temperature Transients Produced by Uncon- trollied Rod Withdrawal, Fuel B. 140 UNCLASSIFLED ORNL DWG, 63.8177 1300 1800 1700 1600 1500 1400 TEMPERATURE (°F) 1300 500 Loo 300 200 POWER (Mw) 100 0 2 Y 6 8 10 12 14 16 TIME (sec) Fig. 12.3, DPower and Temperature Transients Produced by Uncon- trolled Rod Withdrawal, Fuel C. 141 hottest channel, (To)max’ and the highest fuel temperature in the core, (Tf)max' Although the rate of reactivity addition was lower for fuel C than for fuel B, the excursions were more severe for fuel C because of the smaller fuel temperature coefficient of reactivity and the shorter prompt neutron lifetime associated with this mixture. The power excursion oc- curred somewhat later with fuel C because of the greater time required to reach prompt criticality at the lower ramp rate. During steady operation the maximum fuel temperature occurs at the outlet of the hottest channel. However, during severe power excursions which are short compared with the time of transit of fuel through the core, the maximum fuel temperature at a given time may be at a lower elevation in the hottest channel, where the power density is relatively higher. This is illustrated by the difference between the maximum fuel temperature and the temperature at the outlet of the hottest channel during and immediately after the initial power excursion. These two temperatures then converged as the fuel was swept from the region of maximum power density toward the core outlet, while the power was rela- tively steady. The rise in the mixed-mean temperature of the fuel leaving the core is about half of that shown for the hottest fuel channel. The transient calculations were stopped before fihe fuel that was af- fected by the initial power excursion had traversed the external loop and returned to the core. The trends shown in Figs. 12.2 and 12.3 would con- tinue until the core inlet temperature began to rise, about 16 sec after the initial excursion in the outlet temperature. At that time, the power and the outlet temperatures would begin to decrease; the nuclear average temperatures would continue to rise as long as rod withdrawal were con- tinued. However, the rise in graphite temperature resulting from heat transfer from the fuel would reduce the rate of rise of the fuel nuclear average temperature. It is clear from Figs. 12.2 and 12.3 that intolerably high fuel tem- peratures would be reached in this accident if complete withdrawal of the control rods were possible. ©Since the reactor safety system provides for dropping the control rods on high power, the accident involving fuel C was also examined in the light of this action. It was assumed that only 142 two rods dropped (0.1l sec after the flux reached 15 Mw, with an acceler- ation of 5 ft/secz), while the third continued to withdraw. The initial transients for this case are shown in Fig. 12.4. The flat portion in the maximum fuel temperature reflects the time required for the fuel that was heated by the initial excursion to pass out of the core. Dropping two control rods in this accident reduced the temperature excursions to in- significant proportions from the standpoint of reactor safety. Since the reactor cannot be made critical by withdrawing only one control rod, failure of the rod-drop mechanism on one rod does not impair the safety of the system. The core pressure transients were small in all of the rod withdrawal accidents. With no corrective action, the pressure increases were 18 and 21 psi for the cases involving fuels B and C, respectively. Simulation of the control-rod drop limited the pressure excursion with fuel C to 8 psi. 12.7.2 Cold-Slug Accident The kinetic behavior was calculated for a postulated incident in which one core-volume of fuel at 900°F suddenly entered the core, which was initially critical at 1200°F and 1 kw. The resulting power-tempera- ture transients are summarized in Fig. 12.5, as calculated for fuel salt B. The maximum values reached for power and temperature were higher for this case than for salt C. The maximum pressure achieved was about © psi with either salt. The temperature plots given in Fig. 12.5 exhibit the following features: There was an initial 300°F drop in the reactor inlet temper- ature, which remained at 900°F until the core was filled with the cooler fluid. As the volume of the core occupied by the cold slug became larger, the fuel nuclear average temperature decreased slowly, adding reactivity. When the reactivity approached prompt critical, the reactor period became small and substantial nuclear heating occurred. This caused the fuel nu- clear average temperature to rise sharply and limit the power excursion. The additional heat generation was reflected as a rise in the channel outlet temperature. At the time the leading edge of the cold slug reached 143 UNCLASSIFIED ORNL DWG. 63.8178 TEMPERATURE (°F) POWER (Mw) 6 8 10 12 1k 16 TIME (sec) Fig. 12.4. Effect of Dropping Two Control Rods at 15 Mw During Uncontrolled Rod Withdrawal, Fuel C. 144 UNCLASSIFIED ORNL DWG. 638179 1600 1400 400 300 200 POWER (Mw) 100 5.0 10.0 15.0 20.0 25.0 TIME (sec) Fig. 12.5. Power and Temperature Transients Following a 900°F Cold Slug Accident; Fuel Salt B; No Corrective Action. 145 the top of the core, there was a sharp drop in the channel outlet temper- ature. Simultaneously, the reactor inlet salt temperature returned to 1200°F as the available amount of cold fluid was exhausted. The channel outlet passed through a maximum upon arrival of the fluid heated at the center of the core by the initial power transient, then decreased until finally the rise in salt inlet temperature was again reflected {(about 9.4 sec later) as a rise in the channel outlet temperature. It is apparent that the excursions in temperature and pressure re- sulting from the nuclear incident are less important than the rapid rates of change of temperature calculated for the incident. The latter could result in large transient stresses in the inlet and outlet piping and in the fuel pump. 12.7.3 Filling Accident Conditions Teading to Filling Accident. — Normal procedure for start- up of the MSRE requires that the reactor and fuel be heated by electric heaters to near the operating temperature before the fuel is transferred from the drain tank to the core. The control rods normally are partially inserted during a fill, so that the reactor is suberitical at normal tem- perature with the core full of fuel. Criticality is attained by further rod withdrawal after the fuel and coolant loops have been filled and cir- culation has been started. Criticality could be reached prematurely during a startup while the core is being filled if: (a) the control rods were withdrawn from the positions they normally occupy during filling; (b) the core temperature were abnormally low; or (¢) the fuel were abnormally concentrated in ura- nium. Interlocks and procedures are designed to prevent such an accident. If, despite the precautions, the reactor were to become critical under such conditions, there would be a power excursion, the size of which would depend on the source power and the rate of reactivity addition. The core temperature would rise rapidly during the initial power excursion; then, 1f fuel additiofi were continued, it would rise in pace with the increase in critical temperature. The consequences of a number of filling acci- dents were analyzed, and the principal results are summarized in this section. Detailed description of these studies is contained in ref 40. 146 Reactivity Addition., — The amount of reactivity available in a fill- ing accident depends on the conditions causing the accident and the char- acteristics of the fuel salt. In the case of filling the reactor with the control rods fully withdrawn, the excess reactivity is limited to the smount in the normal fuel loading. Only about 3% dk/k will be required for normal operation (see Table 9.1), and the uranium concentration in the fuel will be restricted by administrative control to provide no more than required. Filling at the normal rate with all rods fully withdrawn results in a reactivity ramp of 0.01% 8k/k per second when k = 1. The power excursion assoclated with this ramp is well within the range of control of the rod safety system. Full insertion of any two of the three control rods is adequate for shutdown of the full core. In filling the fuel at an abnormally low temperature, excess reac- tivity is added by means of the negative temperature coefficient of the fuel. TFor fuel B (the mixture with the largest negative temperature co- efficient of reactivity), cooling the salt to the liquidus temperature (840°F) provides 1.9% excess reactivity. The reactivity addition rate at k = 1 is 0,006%/sec. The shutdown margin provided by the control rods is 5.2%, In the case of filling of the reactor core with fuel abnormally con- centrated in uranium, the mechanism assumed to cause the incident is that of selective freezing of fuel in the drain tank., The crystallization paths of all three salt mixtures under consideration are such that large quantities of salt can be solidified, under equilibrium conditions,* be- fore uranium (or thorium) appears in the solid phase. Selective freezing, therefore, provides one means by which the uranium concentration can be increased while the salt is in the drain tank., Since the reactor vessel is the first major component of the fuel loop that fills on salt addi- tions, approximately 40% of the salt mixture can be frozen in the drain tank before it becomes impossible to completely fill the core. The changes in liquid composition as selective freezing proceeds de- pend on the initisl composition and the conditions of freezing. TFigure 12,6 shows the atomic concentrations in the remaining melt for fuel A as *Very slow cooling. 147 UNCLASSIFIED ORNL DWG. 63.8180 0.7 0. 0.05 0.4 0.0k = & 5 g % 0.3 g 0.03 i = g 0. 0.02 0. 0.01 : : ‘ s o 0 0.1 0.2 0.3 0.k 0.5 WEIGHT FRACTION OF SALT FROZEN Fig. 12.6. Ligquid Composition Resulting from Selective Freezing of Fuel Salt A in Drain Tank. a function of the fraction of salt frozen. The curves are based on the assumption that only the equilibrium primary solid phase, €6LiF+BeF;+ZrF,, appears. The effect on premature criticality was evaluated for each of the three salts with 39%, by weight, frozen in the drain tank as 6LiFeBeF- 7ZrF,.* Under these conditions the full reactor at 1200°F had about 4% excess reactivity for fuels A and C and 15% for fuel B. Fuels A and C *The composition of the solid phase has little effect on the nuclear calculations as long as it does not include fissile or fertile material. 148 contain significant amounts of thorium and U238, respectively, which re- main in the melt with the U?33 during selective freezing. The poisoning effect of these species greatly reduces the severity of the filling ac- cident when they are present. The excess reactivities in this accident, with so much selective freezing, exceed the shutdown margin of the con- trol rods. Thus it is necessary to stop the filling process to prevent a second reactivity excursion after the rods have been dropped. The ac- cident involving fuel B is the most severe; the reactivity addition rate for this case is 0.025% ®k/k per second at k = 1, compared with 0.01%/sec for fuels A and C. Corrective Actions. — Control rod drop and stoppage of fuel addition are considered as means for limiting the power excursion and stopping the addition of reactivity. In the first case, dropping the rods on high flux signal (15 Mw power) was found to be more than adequate for any fill- ing accident in which the available excess reactivity does not exceed the shutdown margin of the rods. For the more severe accidents, it is nec- essary to supplement the rod drop by stopping the fill to prevent further reactivity addition. ' Filling the reactor is accomplished by admitting helium, at 40 psig supply pressure, to a drain tank and foreing the liquid fuel up through the drain line into the primary system, Figure 12.7 is a simplified flow- sheet of the reactor fill, drain, and vent systems showing only those features which pertain directly to the filling accident. All valwves are shown in the normal positions for filling the reactor from fuel drain tank No. 1. Three independent actions are available to stop the addition of fuel to the primary loop: 1. Opening HCV-544 equalizes the loop and drain tank pressure. 2, Opening HCV-573 relieves the pressure in the drain tank by venting gas through the auxiliary charcoal bed to the stack. 3. Closing HCV-572 stops the addition of helium to the drain tank. During a filling accident all three actions would be attempted simulta- neously to ensure stopping the fill. The first two actions, in addition to stopping the fill, allow the fuel in the primary loop to run back to the drain tank. Stopping the gas addition only stops the fill, but the salt flow does not stop instantaneously. 149 UNCLASSIFIED ORNL-DWG 63-7320 [ ] FP PCV-522 FHX HOV-V 5§¥A D “r UL K] TO FILTER, FAN, AND STACK FFT REACTOR FO-2 AUXILIARY CHARCOAL FFT BED €D 00 1< > Fv_ FFT FD'ECJ Y ) FD-2 ga&\{ HCV-573 > 1><] 7~ 50-psig DISK FO-2 FFT FD-1 40-psig HELIUM SUPPLY Fig. 12.7. System Used in Filling Fuel Loop. During filling, the flowing fuel in the drain line experiences a small pressure drop. In addition, the gas displaced from the primary loop must flow out to the stack through equipment which imposes some pressure drop. Consequently, the pressure in the drain tank at any point in the filling operation is greater than that required to maintain the liquid- level difference under static conditions. As a result, when gas addition is stopped, the fuel level in the primary loop coasts up until the dynamic head losses have been replaced by an increase in the static head differ- ence between loop and drain tank. If this coast-up occurs during a fill- ing accident, the additional excess reactivity associated with the higher level must be compensated for by the system. 150 Temperature Coefficient of Reactivity. — The temperature coefficient of reactivity of the fuel in the partially filled core differs substan- tially from that in the full system. In the full system, the thermal ex- pansion of the salt expels fuel from the core. The effective size of the core, however, remains essentially constant. Thermal neutron leakage also increases, and both of these factors tend to reduce reactivity. In the partially full core, fuel expansion increases the effective height of the core. This tends to offset the decrease in reactivity due to increased radial neutron leakage. The effective temperature coefficient of reac- tivity of fuel B with the core 60% full is approximately —0.4 X 1072 (°F)™1, compared with —5.0 x 1077 (°F)~1l for the full core. The tempera- ture coefficient of the graphite is not significantly affected by the fuel level. Maximum Filling Accident. - Only the most severe of the postulated filling accidents was analyzed in detail. It was assumed that the uranium in fuel B was concentrated to 1.6 times the normal value by selective freezing of 39% of the salt in the drain tank. Several other abnormal situations were postulated during the course of the accident, as follows: 1. The helium supply pressure was assumed to be 50 psig, the limit imposed by the rupture disk in the supply system, rather than the normal 40 psig. This pressure gave a fill rate of 0.5 £t2/min when criticality was achieved and produced a level coast-up of 0.2 ft after gas addition was stopped. 2. It was assumed that only two of the three control rods dropped on demand during the initial power excursion. 3. It was assumed that two of the three actions available for stop- ping the fill failed to function. Only the least effective action, stop- ping the gas addition, was used in the analysis. This allowed the fuel level to coast up and make the reactor critical after the two control rods had been dropped to check the initial power excursion. The power and temperature transients associated with the accident described abowve were calculated with the aid of both digital and analog computers., ©Since the useful range of an analog computer is only about two decades for any variable, the initial part of the power transient was calculated with the digital kinetics program MURGATROYD, The digital 151 calculation was stopped at 10 kw when the power began to affect system temperatures, and the digital results were used as input to start the analog calculation. Since it was clear that the reactor would go critical again after the control rods had been dropped, the analog simulation in- cluded the compensating effects of the fuel and graphite temperature co- efficients of reactivity. Because of the small fuel coefficient, it was necessary to use a highly detailed model to represent heat transfer from the fuel to the graphite during the transient. The results of the maximum fill accident simulation are shown graph- ically in Figs. 12.8 and 12.9. Figure 12.8 shows the externally imposed reactivity transient exclusive of temperature compensation effects. The essential features are the initial, almost-linear rise which produced the first power excursion as fuel flowed into the core, the sharp decrease as the rods were dropped, and the final slow rise as the fuel coasted up to ite equilibrium level., TFigure 12.9 shows the power transient and some pertinent temperatures. The fuel and graphite nuclear average tempera- tures are the quantities which ultimately compensated for the excess re- activity introduced by the fuel coast-up. The maximum fuel temperature refers to the temperature at the center of the hottest portion of the hottest fuel channel. The initial power excursion reached 24 Mw before being checked by the dropping control rods, which were tripped at 15 Mw, This excursion is not particularly important, because it did not result in much of a fuel temperature rise. After the initial excursion, the power dropped to about 10 kw and some of the heat that had been produced in the fuel was transferred to the graphite., The resultant increase in the graphite nuclear average temperature helped to limit the severity of the second power excursion., Reactivity was added slowly enough by the fuel coast-up that the rising graphite temperature was able to limit the second power excursion to only 2.5 Mw. The maximum temperature attained, 1354°F, can be tolerated for long times. 12.7.4 Fuel Pump Power Failure The consequences of Interruption of fuel circulation while the re- actor is at high power were determined by analog computer simulation of NET REACTIVITY (%) 1.0 0.% -1.0 152 UNCLASSIFIED ORNL DWG, 63.8181 =0 100 150 200 C 2% 300 350 Net Reactivity Addition During Maximum Filling Accident. 153 UNCLASSIFIED ORNL DWG. 63.8182 1360 1320 1280 = 1240 +F TEMPERATURE (°F) 1200 = POWER (Mw ) 0 oy 100 150 200 250 300 390 TIME (sec) Fig. 12.9. Powver and Temperature Transients Following Maximum Filling Accident. 154 the nuclear, heat transfer, and thermal convection equations for the sys- tem. Failure of the fuel pump power supply, with subsequent coast-down of the flow, was simulabted by causing the circulation rate to decrease exponentially with a 2-sec time constant until it reached the thermal circulation rate determined by the temperature rise across the core. As the fuel circulation rate decreased, the effective delayed neutron frac- tion was increased by 0,003 and the heat transfer coefficient in the heat exchanger was reduced. Figure 12.10 shows the results of a simulated fuel pump failure at 10 Mw, with no corrective action. The gain in delayed neutrons caused the initial rise in the power. The decrease in heat removal from the core, coupled with the high production, caused the core outlet tempera- ture to rise. As the fuel flow and the heat transfer in the heat ex- changer fell, the continued heat extraction at the radiator caused the coolant salt temperature to decrease and reach the freezing point in less than 2 min, (The behavior in simulator tests at lower power was similar, but the coolant temperature remained above the freezing point if the ini- tial power was less than 7 Mw.) Practical measures can be taken to prevent freezing of the coolant salt or overheating of the core in the event of fuel pump failure. These consist of closing the radiator doors and inserting the control rods, Figure 12.11 shows simulator results for a case in which these actions were taken rather slowly, yet proved effective. One second after the pump power was cut, a negative reactivity ramp of —0.075% 8k/k per second was initiated, simulating insertion of the control rods at normal driven speed, Beginning 3 sec after the pump power failure, the simulated heat removal from the radiator tubes was reduced to zero over a period of about 30 sec. 12.7.5 Conclusion The results of the analyses described here form part of the basis for a comprehensive analysis of the safety of the reactor system. The credibility and the importance of each accident are evaluated and dis- cusged in the Safety Analysis Report. 155 UNCLASSIFIED ORNL-LR-DWG 67578 f T f 1 t | 1400 T ""’i _/ - -‘---'-—-—.__\ ‘ CORE OUTLET ‘ // ————__| CORE FUEL MEAN 1300 /‘// ’”>\\ | A e SV T GRAPHITE MEAN . 1200 _ — e — — e o = e ——— INLE l . " ~—|__CORE INLET } :) .-._-—- ! — § 1100 ' w Ty I t ] a RADIATOR INLET w | — \\ ! 1000 . 7 i \_____ \\ \ \ \ \ 900 ——— o SALT LEAVING RADIATOR =] — — -..g-: 800 12 1 /- 10 \\ \\QSWER — 8 = = N & 6 \ = \ O a 4 k\ 0 0 20 40 60 80 100 120 TIME (sec) Fig. 12.10, Power and Temperature Transients Following Fuel Pump Power Failure at High Power; No Corrective Action. 156 UNCLASSIFIED ORNL-LR-DWG 67579 1300 CORE QUTLET GRAPHITE MEAN w ° ° 1200 E FUEL MEA w 5 CORE INLET — < o w & 1oo = RADIATOR INLET — RADIATOR OUTLET 1000 DIATO - FISSION POWER 3 = a L = O c. 0 20 40 60 80 100 120 TIME (sec) Fig. 12.11. Power and Temperature Transients Following Fuel Pump Power Failure at High Power; Radiator Doors Closed and Control Rods Driven in After Failure. 157 13. BIOLOGICAL SHIELDING 13.1 General The basis for the design of all biological shielding is the recom- mended maximum permissible exposure to radiation of 100 mrem/week, or 2.5 mrem/hr based on a 40-hr work week. The criterion for the MSRE biological shield design is that the dose rate will not exceed 2.5 mrem/hr during normal operation at any point on the shield exterior that is located in an unlimited access area. This criterion inherently includes allowance for significant underestimation of the hot-spot dose, with the general area still below 2.5 mrem/hr. As in most reactor designs (and particularly in the case of the MSRE, since it has to fit within an existing reactor contaimment cell and build- ing) nuclear, mechanical, and structural requirements, ag well as eco- nomics, preclude the design of permanently installed shielding that re- sults in a dose rate that is less than the permissible rate at all points. Consequently, the final shield design allows for addition of shielding as needed to reduce the radiation level at localized hot spots. 13.2 Overhead Biological Shielding The calculations which are described in this section on the biolog- ical shielding over the reactor cell were carried out at an early stage of the design.4l The source strengths which were used, and which are re- ported in this section, differ somewhat from those obtained from the latest nuclear calculation (see Sec 13.3.4 for later results). The dif- ferences would make no significant change in the prescribed shielding. In this section, the calculations sometime refer to ordinary concrete, which was initially considered for use. The final shield design is com- posed of barytes concrete, ordinary concrete, and steel which is equiva- lent to about 9 ft of ordinary concrete and about 7 £t for neutrons. 13.2.1 Geometry The basic shield construction is shown in Fig. 13.1., Two separate layers of concrete blocks are used; the majority of the lower blocks are 158 UNCLASSIFIED ORNL—DWG 63-7321 -+—— BILOG NORTH - Y -in. MAX. BLOCK SPACING 1 AT e . N TR BN |5 3ft 6in.)|| : . : UPPER SHIELD BLOCKS e . - - o f] a T . - ) s e s g e o L e o . - - . - « e - + N Subscripts: S o m o= O P Distance from source to dose point Buildup factor Dose rate Attenuation functions, tabulated in TID-700442 Attenuation functions, tabulated in TID-700442 Source length Concentration per unit volume Production rate per unit volume Radius of disk or cylindrical source Source strength, number per unit time per unit area, or unit volume Regidence time Regidence time Time and thickness Gap width Self absorption distance Decay constant Attenuation coefficilent Particle flux Annmulus Core Lower header source Total Upper header 179 14. MISCELLANEQOUS 1l4.1 Radiation Heating of Core Materials Heat produced in the graphite by absorption of beta and gamma ra- diation and the elastic scattering of fast neutrons amounts to about 7% of the total heat produced in the reactor. This heating of the graphite affects the overall kinetic behavior of the reactor through its effect on graphite temperature response. Heat produced in the INOR parts of the reactor, on the other hand, is a small fraction of the total and has little effect on overall behavior. It is important, however, from the standpoint of local temperatures. The spatial distribution of the graphite heating was computed, with the results shown in Figs. 14.1 and 14.2. In these computations the main part of the core was treated as a homogeneous mixture, with gamma energy being absorbed at the point of origin. (This is a reasonable approximation for the MSRE, because the core is large and the channels are small in relation to the mean free path of gamma rays.) Capture gammas from the INOR control rod thimbles and core support grid were treated separately, because the sources were quite concentrated. Gamma-ray heating of INOR at a number of points on and inside the reactor vessel was computed with digital computer codes NIGHTMARE*? and 20GH?C (a two-dimensional version of NIGHTMARE). These computations ob- tained the gamma flux at one specified point by summing the contributions of gammas originating in all parts of the reactor, using appropriate attenuation and buildup factors. A multiregion model of the reactor similar to that described in Sec 3.2 was used in these computations. Values of gamma sources per fission and per capture were taken from ref 49. The source of fission product decay gammas was assumed to follow the same spatial distribution as the fissions. Results of these calcu- lations are given in Table 14.1. A summary of the nuclear energy sources and the places where the energy appears as heat is given in Table 14.2. The total energy which heats the fuel as it passes through the reactor vessel is 196.7 Mev per fission. 180 UNCLASSIFIED DRNL DWG, 63-8185 HEATING (w/cc) 0 L 8 12 16 20 2l 28 RADIUS (in.) Fig. 14.1. Heating in Graphite: Radial Distribution near Midplane at 10 Mw. 181 UNCLASSIFIED ORNL DWG. 63-8186 0.7 0.6 0.5 0.4 o L = 2 H % 0.3 0.2 0.1 0 10 20 30 Lo 50 60 70 A¥IAL POSITIOK (in.) Fig. 14.2. Heating in Graphite: Axial Distribution 8.4 in. from Core Center Line at 10 Mw. 182 Table 14.1. Gamma Heating of INOR in MSRE, Operating at 10 Mw Heat Source Calculation Location (w/em?) Method Reference Rod thimble, midplane 2.5 NIGHTMARE 7 Core can, midplane 0.2 NIGHTMARE “ Vessel, midplane 0.2 NIGHTMARE & Upper grid 2.2 NIGHTMARE 4 Lower grid 1.8 NIGHTMARE 4 Upper head at fuel outlet 0.1 2DGH 50 Table 14.2. Energy Sources and Deposition in MSRE Energy (Mev/fission) Absorbed source Emitted Fuel Cell . . Graphite and Main Perlpheral External shield Core Regions Fission fragments 168 149.5 18.5 0 0 0 Fast neutrons 4.8 0.8 0.1 C 3.5 0.4 Prompt fission 72 1.9 0.7 C 445 0.1 gammas Fission product 5.5 0.7 2.2 0.7 1.6 0.3 decay gammas Fission product 8.0 2.7 3.0 1.3 1.0 0 decay betas Capture gammas 6.2 1.2 242 0 2.6 0.2 Neutrinos 11 0 0 0 0 0 210.7 156.8 2647 2.0 13.2 1.0 183 14.2 Graphite Shrinkage At the temperature of the MSRE core, fast-neutron irradiation causes graphite to shrink. Shrinkage is proportional to the total exposure and is greater in the direction of extrusion than in the direction normal toO the axis of extrusion. Thus shrinkage will be nonuniform, leading to changes in the core dimensions and the distribution of fuel and graphite within the core. These changes produce slow changes in reactivity. Available information on the behavior of MSRE graphite under nuclear irradiation did not permit a detailed analysis, but some of the reactivity effects were estimated, using preliminary information. The coefficient for shrinkage parallel to the axis of extrusion (axial shrinkage) for a grade of graphite similar to that to be used in the MSRE is about 2.06 X 10—2% per nvt for neutrons with energies greater than 0.1 Mev. The co- efficient for EGCR graphite in the seme temperature range, between 5 and 8 x 10?1 nvt of neutrons with energies greater than 0.18 Mev, is about 1.8 x 10™2% per nvt. Also, for EGCR graphite the coefficient for shrink- age normal to the extrusion axis (transverse shrinkage) is about half that for axial shrinkage. On this basis the coefficients used in the analysis described below were 2.06 X 1024 and 1.0 X 102%* per nvt (E > 0.18 Mev) for axial and transverse shrinkage, respectively. The neutron flux distributions for energies greater than 0.18 Mev calculated for fuel C were used (see Figs. 3.9 and 3.10). All of the reactivity effects were based on one full-power year of reactor operation. Since the MSRE graphite stringers are mounted vertically, axial shrinkage causes, first of all, a shortening of the moderated portion of the core. The amount of shrinkage in individual stringers depends on the radial distribution of the fast flux, so that the top of the graphite structure will gradually take on a dished appearance. The maxinum axial shrinkage was estimated to be about 0.1l4 in./yr. Even if the entire moderator structure were shortened by this amount, the effect on reac- tivity would not be detectable. In addition to shortening the stringers, axial shrinkage increases the effective graphite density in the main portion of the core. The total axial shrinkage is equivalent to a uni- form density increase of 0.11% per year. This corresponds to a reactivity 184 increase of 0.08% Ak/k per year. The nonuniformity of the density change might increase the reactivity effect by as much as a factor of 2, but the resultant effect would still be negligible. A third effect of axial contraction is bowing of the stringers, caused by the radial gradient in the neutron flux. This mechanism leads to an increase in the fuel volume fraction in the main portion of the core and has the same effect as increasing the fuel density. The maximum bowing has been estimated at 0.1 in./yr.51 If it is assumed that the bowing causes a uniform radial expansion of the graphite assembly, this rate represents an equivalent increase in the fuel density of 3.2%/yr. The associated reactivity effect is 0.6% Ak/k per year. Since both ends of the graphite stringers are constrained from radial motion, uniform expansion of the assembly will not occur. Instead, the stringers which have the greatest tendency to bow will be partly restrained, while others, in regions where the radial flux gradient is smaller, will be bulged out- ward at the middle. The net result will be a much smaller fractional in- crease in fuel volume than would be predicted for a completely uncon- strained assembly. Shrinkage of the graphite transverse to the direction of extrusion adds to the effect produced by bowing. However, this effect 1s much smaller because of the smaller shrinkage coefficient. The calculated re- activity effect was 0.04% Ak/k per full-power year of operation. 14.3 Entrained Gas in Circulating Fuel 14.3.1 Introduction The nuclear characteristics of the reactor are affected by the presence of entrained helium bubbles, which circulate with the fuel through the core. This gas, introduced through the action of the fuel spray ring in the fuel circulating pump, reduces the effective density of the fuel and makes the fuel-gas mixture compressible. The most im- portant consequence is that there is a pressure feedback on reactivity, which is positive for rapid changes in pressure and temperature and negative for slow changes. 185 14.3.2 Injection and Behavior of Gas A small fraction of the fuel pump discharge stream (50 gpm out of 1250 gpm) is diverted into a spray ring in the gas space in the pump bowl. The purpose of the spray, or stripper, is to provide contact so that Xe'?’ in the salt can escape into the gas space, which is continu- ously purged. Salt Jetting from holes in the spray ring impinges on the surface of the liquid pool in the pump bowl with sufficient velocity to carry under considerable quantities of gas, and some of the submerged bubbles are swefit through the ports at the pump suction into the main circulating stream of fuel. A steady state is reached when the helium concentration in the circulating stream has increased to the point where loss of helium through the stripper flow equals the rate of injection. At steady state the volume fraction of gas in the circulating stream varies around the loop with the inverse of the local pressure, which changes with elevation, velocity, and head losses. Pump loop tests showed a volume fraction of 1.7 to 2.0% gas at the pump suction, which is normally at 21 psia in the reactor. In the core, where the pressure ranges from 39.4 psia at the lower ends of the fuel channels to 33.5 psia at the upper ends, the equivalent volume fraction of gas is about 1.2%. Yor rapid changes in core or loop pressure, the mass ratio of gas to liquid remains practically constant and the volume fraction of gas in the core decreases with increasing pressure. For very slow increases in 1loop pressure the volume of gas in the core increases, because the ratio of absolute presgures between the core and pump suction is reduced. (The steady-state volume fraction at the pump suction is presumably independent of pressure.) 14.3,3 Effects on Reactivity The presence of the gas in the core has two effects on reactivity. First, by making the fuel compressible, the gas introduces a pressure coefficient of fuel density or reactivity. Secondly, the presence of the gas modifies the fuel temperature coefficient of reactivity, because the density of the salt-gas mixture changes with temperature at a different rate from the density of the salt alone. 186 A detailed description of the reactivity effects of entrained gas involves the following quantities: f Volume fraction of gas in fuel stream at pump suction Absolute pressure in the core Pg Absolute pressure at the pump suction T Temperature of the fuel in the core g Volume fraction of gas in fuel in core Py Density of liquid salt containing no gas Pe Density of the fuel salt—gas mixture 1 9% — ='5;T§f_ Temperature coefficient of salt density pg Ok . . B = 85;_ Fuel density coefficient of reactivity —y Contribution to fuel temperature coefficient of re- activity due to changes in neutron energies and microscopic cross sections The core pressure is related to the reactivity through the mean fuel density in the core: 1 ok 1 Bpf E5§=B¥ S - (14.1) The fuel temperature affects the reactivity through the fuel density and also through its effect on thermal neutron energy and microscopic cross sections: 1 dk 1 Bpf EB—T-=B'5;5T—7. (14.2) The mean density of the fuel is given by pp = (L= 08)o, . (14.3) (The gas adds practically nothing to the fuel density.) If there is no gas in the core, 6 = 0, P = Pys and the effect of pressure on density is negligible. With no gas in the fuel, e 187 d 5%—= -0 - 7 . = |- Rapid Changes. — During rapid changes in pressure and temperature, the mass ratio of gas to liquid remains practically constant. (The change in the amount of dissolved helium is negligible compared with the amount in the gas phase.) In this case Pe is approximated by [1 - (T ~ Tp)] Pe = By 7 G5 T pflo , (14.4) where the subscript O refers to initial conditions. If Eg. (14.4) is used to obtain the partial derivatives of Ps required in (14.1) and (14.2), these eqguations become 8[1 — (T — To)] 1 ok _ ES (1 - 90> T, T } (14.5) [l—@(T“To)+ T E‘*fi—a P and (-2 a) 190k _ —op - TPt o)P —~ (14.6) k of 1 - T — Tg) <1 - 90> To 27 ' l—Q',(T'—To)-F ——e—o'-— —T—P—O At the initial point, when P = Pg and T = Ty, 1 ok POy =5 Z-E%— (14.7) and 1 ok 1 _kfi—w+7+<fl—a> 6o0B . (14.8) These equations show that for rapid changes there is a positive pressure coefficient of reactivity and that the magnitude of the negative tempera- ture coefficient of reactivity is increased because the gas expands more than the liquid (1/Ty is greater than Q). Slow Changes. — During gradual changes in fuel loop temperatures and pressure, f will probably remain equal to the volume fraction in the pump 188 bowl just outside the ports, which should be constant. The core mean pres- sure is 15.6 psi higher than the pump suction pressure; therefore 0 =f 2 = f(P‘_PU'_@) , (14.9) op = (1 -+ 5 %). (14.10) If the partial derivatives of Pp required in Egs. (14.1) and (14.2) are obtained from Eq. (14.10), Egs. (14.1) and (14.2) become 1 ok - e . _Sf‘ = (14.11) P +( 7 >15.6 and Sk ' %fi =—ag -7y . (14.12) Thus for slow changes, there is a negative pressure coefficient of reac- tivity and the temperature coefficient is the same as if there were no entrained gas. Magnitude. — The magnitudes of pressure and temperature coefficients of reactivity with entrained gas in the core are listed in Table 14.3 for three different fuel salts, at the conditions listed at the bottom of the table. Importance. — During normal operation, the presence of entrained gas introduces additional reactivity “noise" because its compressibility con- verts fluctuations in core outlet pressure drop to reactivity perturba- tions. In power excursions, the gas enhances the negative temperature coefficient of reactivity. At the same time it superimposes a pressure coefficient which makes a positive contribution to reactivity during at least part of the power excursion. (See Sec 12.4.3 for discussion of pressure behavior during power excursions.) In any credible power excur- sion, the pressure rise, in psi, is numerically much smaller than the fuel temperature rise, in °F, and the net reactivity feedback from pressure and temperature is negative. 189 Table 14.3. Reactivity Coefficients with Entrained Gas in Core® Fuel A Fuel B Fuel C Fuel density coefficient of 0.1290 0.345 0.182 reactivity, B ol (°F)™] —2.24 x 10™° —4,07 x 10™° —=2,15 x 1077 y[(°F)™*] —0.79 x 10~ —0.90 x 10~% —1.13 x 107 Fuel temperature coefficient of reactivity [(°F)™] No gas or slow changes —3.03 x 107" —4.97 x 10™° =3.,28 x 10~° with gas Rapid changes with gas —3.14 x 1077 —5.17 x 107> =3.39 x 1077 Pressure coefficient of reactivity (psi~t) Slow changes with gas -3.8 x 107° 7.0 x 107 =3.7 x 10~ Rapid changes with gas +6.3 X 10™° +11.4 x 107 +6.0 x 10~ aEvaluated at T e = 00012, and. X = lo M 14.4 Choice of Poison Material =136.5 psia (pump bowl pressure 5 psig), There is avalilable a wide variely of materials that have been used as neutron absorbers in reactor control rods. The choice of poison ma- terial for a given reactor application must be based primarily on the overall sultability of the poison, considering the physical and chemical, as well as the nuclear, environment. If several acceptable materials exist, the choice between them may be made on the basis of cost and ease of procurement of the required form. 14.4,1 Boron The first poison material considered for use in the MSRE was boron because of its low cost, ready availability, and high neutron-capture cross section in both the thermal and epithermsal energy ranges. 190 The shape of the poison elements was established by the mechanical design of the rod assemblies, which required short, hollow cylinders of poison. Pure boron carbide (B,C) was tentatively selected as the poison material, to ensure long rod life. This material could easily be fabri- cated in the desired shape and also have the stability against thermal decompesition required for use at reactor temperatures. However, B,C is highly abrasive and oxidizes in air at high temperature. These proper- ties made it necessary to consider complete canning of the poison elements. Essentially all of the poisoning by B,C is due to neutron absorptions in B0, where the predominant reaction is B®(n,x)Li?. The alpha particle ends as a helium atom, so that each neutron absorption results in the re- placement of a single atom by two of approximately the same size. This effect alone would lead to significant damage, due to volume increase in the poison elements after long exposure. Howefer, the difficulty i1s com- pounded, particularly in the case of canned elements, by the fact that one of the nuclear reaction products is a gas. Only a fraction of the helium produced escapes from the poison elements, but this fraction in- creases with increasing neutron exposure. In addition, the amount escap- ing cannoct be predicted reliably. Therefore, to be conservative, all cal- culations of gas pressure buildup were based on the assumption that all of the gas escapes. Calculations of the helium production rate in the MSRE control rods indicated that the rod life would be severely limited by the pressure buildup in completely sealed poison capsules. Since it appeared infeasible to vent the capsules because of the oxidation problem, the use of B,C was abandoned in favor of a more radiation-stable material. 14.4.2 Gadolinium The poison material finally selected for use in the MSRE was gadolin- ium, fabricated in ceramic cylinders containing 70 wt % Gdp03 and 30 wt % A1,05. This material has satisfactory nuclear properties and was selected over other, equally suitable materials on the basis of its moderate cost, ready avallability, and the fact that it could be used without additional development. Natural gadolinium has two isotopes (155 and 157) with extremely large thermal neutron-capture cross sections; the average 2200 m/sec 191 cross section for natural gadolinium is 46,600 barns. However, the neu- tron~capture products of both isotopes are stable gadolinium isotopes with very low cross sections, so that the neutron-capture efficiency is very low, about 0.3 neutrons per atom of natural gadolinium. Gadolinium also has a relatively low capture cross section for resonance-energy neu- trons (about one-fourth that of boron). Thus, for rods which are "black" to thermal neutrons, a boron~containing rod will control somewhat more reactivity than one containing gadolinium. Because of the large cross section, only a small amount of gadolin- ium is required for "blackness" to thermal neutrons. However, this same property results in very rapid burnout of a rod that is initially just barely "black." Therefore, such a rod must have built into it sufficient gadolinium to ensure that it remains "black" throughout its required life- time. The low neutron-capture efficiency requires relatively large amounts of gadolinium for this purpose. The individual ceramic poison capsules on the MSRE control rods are 0.84 in. ID by 1.08 in. OD by 1.315 in. long. The elements contain about sixty times the concentration of gadolinium required for “blackness" to 1200°F thermal neutrons. This is sufficient to maintain "blackness" in those portions that are continuously exposed to the neutron flux for the equivalent of about 50,000 full-power hours. Since the end products of neutron absorption in gadolinium are other isotopes of the same element, there is essentially no volume change associ- ated with its exposure to neutron bombardment. As a result this material may be expected to have reasocnable resistance to radiation damage; at least the problem of gas production associated with the irradiation of boron is avoided. Structural strength of the poison is of secondary importance, because the elements are completely canned. However, completely leak-proof canning is less important with Gd;0s; than with B,C, because of the greater chemical stability of the former. 14.5 Criticality in Drain and Storage Tanks Molten fuel salt with the uranium concentration required for criti- cality in the core is not critical in the drain tanks or the storage tank, This is s0 because there 1s much less moderator in the tanks than in the 192 core and the tanks are of smaller diameter than the core, and these ef- fects outweigh the increased fuel volume fraction in the tanks. Normally, when fuel salt is stored in either the drain tanks or the storage tank, it is kept in the molten state. However, under some condi- tions it may be desirable to allow the salt to solidify in a tank and coocl to ambient temperature. Simply cooling the salt causes the reac- tivity to increase because of the increased density and cross sections. In addition, if the salt is cooled extremely slowly, it is possible for a nonuniform composition to develop, with the uranium tending to be more concentrated in the remaining melt as the slow freezing progresses. It is conceivable that slow freezing could begin at the outside surfaces, leading to a condition in which the uranium is all concentrated in a cen- tral region surrounded by a neutron-reflecting layer of barren salt. Some additional neutron reflection would occur if the cell containing the tank were flooded with water. (The effectiveness of the water reflector is limited by the furnace structure which surrounds each of the tanks.) Under such abnormal conditions, criticality in the tanks is not impossible. In order to outline the limiting conditions for criticality in the tanks, some calculations were made with the multigroup neutron diffusion program MODRIC. Effective multiplication constants were calculated for fuels B and C in the drain and storage tanks, at 20°C, for various degrees for uranium segregation.’? A major uncertainty in these calculations was the density of the salt. In the absence of experimental information, a conservative approximation was made by computing the density of the un- segregated salt from the x-ray densities of the components. (The actual density should be lower because the salt will not be a perfect crystal, and cracks and voids will probably develop as the frozen salt cools.) Calculations were made in both cylindrical and spherical geometry for the case of uniform concentration, with the size of the sphere chosen to give the same multiplication as in a cylinder having the actual dimensions of the tanks. Calculations were made in spherical geometry with the uranium concentrated by factors of 2, 4, and 10. In these cases, the uranium and a stoichiometric amount of fluorine were assumed to be uniformly dispersed 193 in a sphere surrounded by a layer of uranium-free salt. The concentra- tions of the other components were assumed to be uniform in both the fueled and unfueled portions. The results of the calculations are shown graphically for the storage tank and a fuel drain tank in Figs. 14.3 and l4.4, respectively. If all other conditions are equal, the reactivity is higher in the storage tank than in a drain tank, because of the INOR coolant thimbles in the latter. In the reflected cases, a practically infinite (50 em) Ho0 reflector was assumed., This gives an overestimate of keff’ since the effective reflec- tor thickness must be less because of the furnace. The amount of over- estimation is not great, however, as shown by the comparison of the curves for fuel B in the storage tank, bare and reflected. In one calculation the salt density was assumed to be 95% of the upper limit used in the other calculations. This was for the case of fuel B, concentrated by a factor of 10 in the reflected storage tank, and gave a keff of 1.003, com- pared with 1.024 for the higher density. Similar reductions might be ex~- pected for the other cases, 194 UNCLASSIFIED ORNL DWG. 63-8187 FUEL C, REFLECTED FUEL B, REFLECTED FUEL B, 1‘:ef':f‘ 1 2 L 6 8 10 URANTUM CONCENTRATION FACTOR Fig. 14.3. Effect of Uranium Segregation on Criticality in Fuel Storage Tank at 20°C. 195 UNCLASSIFIED ORNL DWG, 638188 1. FUEL C, REFLECTED 1. 1.00 FUEL B, REFLECTED 0.96 G4 H Q L 0.92 0.88 0.84 0.80 0.76 0 1 2 k 6 8 10 URANTUM CONCENTRATION FACTCR Fig. l4.4. BEffect of Uranium Segregation on Criticality in Fuel Drain Tank at 20°C. 196 i 15. REFERENCES - 1. C. L. Davis, J. 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Goldstein, Fundamental Aspects of Reactor Shielding, p. 60, Addison-Wesley, Reading, Mass., 1959, 44e Do J. Hughes and R. B. Schwartz, "Neutron Cross Sections," USAEC - Report BNL-325, Brookhaven National Laboratory, July 1, 1958. 45, C. W. Nestor, Jr., Oak Ridge National Laboratory, unpublished data, May 196l. $ 46, B, P, Blizard, "Neutron Radiation Shielding," ORNL publication for ORSORT text, September 17, 1956, 47, B, Troubetzkoy and H. Goldstein, "Gamma Rays from Thermal Neu- tron Capture,"” Nucleonics, 18(11): 171~173 (November 1960). 48. P, N, Haubenreich and B. E. Prince, Oak Ridge National Labora- tory, personal communication to H., C. Claiborne, Oak Ridge National Labo- ratory. 9. M. L. Tobias, D. R. Vondy, and Marjorie P. Lietzke, "Nightmare — An IBM 7090 Code for the Calculation of Gamma Heating in Cylindrical Ge- ometry," USAEC Report ORNL-3198, Oak Ridge National Laboratory, February 9, 1962. 50, Oak Ridge National Laboratory, "MSRP Semiann. Progr. Rept. Feb. 28, 1962," USAEC Report ORNL-3282, pp. 68—71. 51. 8. E. Moore, Oak Ridge National Laboratory, personal communica- tion to R. B. Briggs, Oak Ridge National Laboratory (April 26, 1962). 52. J. R. Engel and B. E. Prince, "Criticality Factors in MSRE Fuel Storage and Drain Tanks," USAEC Report ORNL ™~ _, Oak Ridge National Laboratory (in preparation). 14. 15. 16. 17. 18. 19. 20. 21. 22 23. 24 . 25. 26. 27. 28 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39-48. 49, 50. 51. 52. 53. 94-95, %. 97. o8. 99. 100-114. 199 ORNL TM-730 INTERNAL DISTRIBUTION Central Research Library 54, J. W. Krewson . ORNL — Y-12 Technical Library 55. J. A. Lane Document Reference Section 56. C. E. Larson Reactor Division Library 57. R. B. Lindauer Laboratory Records Department 58, M. I. Lundin Laboratory Records, ORNL R.C. 59. R. N. Lyon R. G. Affel 60. H. G. MacPherson . L. G. Alexander 61l. W. B. McDonald C. F. Baes 62. H. F. McDuffie S. E. Beall 63. C. K. McGlothlan M. Bender 64. W. R. Mixon E. 8. Bettis 65. R. L. Moore F. F. Blankenship 66. P. Patriarca R. Blumberg 67. He R. Payne R. B. Briggs 6&8. A. M. Perry S. Cantor 69. B. E. Prince H. C. Claiborne 70. J. L. Redford J. A. Conlin 71. M. Richardson W. H. Cook 72. R. C. Robertson L. T. Corbin 73. M. W. Rosenthal G. A. Cristy 74. He We. Savage Jd. L. Crovwley ‘ 75. J. E. Bavolainen J. H. DeVan 76. D. Scott S. J. Ditto 77. J. H. Shaffer R. G. Donnelly 78. M. J. Skinner N. E. Dunwoody 79. A. N. Smith J. R. Engel g0. P. G. Smith E. P. Epler 8l. I. Spiewak J. E Frye , 82. J. A. Swartout R. B. Gallaher 83. A. Taboada W. R. Grimes 84. J. R. Tallackson A. G. Grindell 85. R. E. Thoma R. H. Guymon 86. D. B. Trauger P. H. Harley 87. W. C. Ulrich P. N. Haubenreich 88. C. F. Weaver E. C. Hise 89. H. S. Weber P. P. Holz 90. B. H. Webster J. P. Jarvis 91. A. M. Weinberg R. J. Kedl 92. J« C. White S. 8. Kirslis 93. L. V. Wilson EXTERNAL DISTRIBUTION D. ¥. Cope, Reactor Division, AEC, ORO R. L. Philippone, Reactor Division, AEC, ORO H. M. 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