An Improved Fission Product Pressure Model for Use in the Venus-II Disassembly Code

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1 Brigham Young University BYU ScholarsArchive All Theses and Dissertations An Improved Fission Product Pressure Model for Use in the Venus-II Disassembly Code Ray Leland Jensen Brigham Young University - Provo Follow this and additional works at: Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Jensen, Ray Leland, "An Improved Fission Product Pressure Model for Use in the Venus-II Disassembly Code" (1976). All Theses and Dissertations This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu, ellen_amatangelo@byu.edu.

2 [ l 0, G$l r< j I $ i ( i. * '**? J. AN IMPROVED FISSION PRODUCT PRESSURE MODEL FOR USE IN THE VENUS-II DISASSEMBLY CODE A Thesis Presented to the Department o f Mechanical Engineering Brigham Young U n iv e rs ity In P a rtia l F u lfillm e n t o f the Requirements fo r the Degree Master o f Science by Ray L. Jensen A p ril 1976

3 This th e s is, by Ray L. Jensen is accepted in i t s present form by the Department o f Mechanical Engineering o f Brigham Young U n iv e rs ity as s a tis fy in g the th e s is requirem ents fo r the degree o f Master o f Science. Date Typed by: Joan Beckstrom i i

4 TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS... LIST OF T A B L E S... iv v ACKNOWLEDGEMENTS... v i Chapter I. INTRODUCTION... 1 I I. PREDICTED OF THE EQUILIBRIUM PRESSURES... 6 The Noble Gases... 8 The A lk a li M e ta ls... 9 The Remaining F ission Products I I I. RELEASE AND PRESSURIZATION PARAMETERS S p a tia l R etention Modeling P re s s u riz a tio n Under T ra n sie n t C onditions IV. THE EFFECTS OF THE FISSION PRODUCT PRESSURES IN SAMPLE DISASSEMBLY CASES V. SUMMARY AND CONCLUSIONS APPENDIX A APPENDIX B APPENDIX C REFERENCES i i i

5 LIST OF ILLUSTRATIONS Figure Block Diagram on V E N U S -II... C alculated Pressures o f A lk a li M etals f o r 3% Burnup.... Page C alculated Pressures o f the Remaining Products fo r 3% Burnup... Temperature D is trib u tio n in Fuel Pin... Bubble T r a ils in Columnar Grains o f Fuel Rod... Irra d ia te d Fuel Element Showing C entral V oid, Columnar Grain Growth, and Typical Reactor S ta rtu p and Shutdown Cracks... Sample o f th e Various R etention P ro file s th a t can be Obtained w ith the F ission Product Pressure Model... P re s s u riz a tio n Rates w ith D iffe re n t Delay Times... Total Energy Release as a Function o f Time... Displacement R e a c tiv ity as a Function o f Time... Total Energy Release as a Function o f Time... Displacement R e a c tiv ity as a Function o f Time... Total Energy Release as a Function o f Time... Flow C hart o f F ission Product Pressure Model in the VENUS-II Disassembly Code iv

6 LIST OF TABLES Table Page 1. Summary o f R e la tiv e Energy Releases Sample o f Tabulated Pressures as C alculated in Reference v

7 ACKNOWLEDGEMENTS The author wishes to express his sincere a p p re c ia tio n to Dr. James Jackson fo r the o p p o rtu n itie s and assistance th a t he has provided to make th is th e sis a r e a lit y. His continued encouragement and advice was an e s s e n tia l element in the successful te rm in a tio n o f th is work. A special thanks is extended to the fa c u lty and s t a f f o f the Mechanical Engineering Department. The help o f Drs. Howard S. Heaton, John N. Cannon and James H. Polve was g re a tly appreciated. The assistance o f Joan Beckstrom in preparing the paper was an e sse n tia l help. The p a tience, support, and assistance o f my dear w ife, C h a rlo tte, helped me through the rougher stages o f my work. Her tender word o f encouragement prodded me on to a successful com pletion. Last but not le a s t my parents are also to be thanked fo r th e ir continued support and encouragement. I a ttr ib u te much o f my success to the e a rly tra in in g th a t I received concerning the value o f a jo b w ell done. To them I extend my sincere love and respect.

8 CHAPTER I INTRODUCTION The w o rld 's growing need fo r safe, r e lia b le, and long-term energy sources has in te n s ifie d the research being conducted in the development o f nuclear power. The operation o f power re a cto rs is co n tin g e n t upon the continued a v a ila b ilit y o f the f i s s i l e m a te ria l re q uire d to m aintain a c r i t i c a l re a c to r. The o nly n a tu ra lly occuring f i s s i le m a te ria l is an isotope o f uranium, U-235, which o n ly accounts fo r 0.76 percent o f the uranium th a t is mined. Due to the r e la tiv e s c a rc ity o f th is im portant f i s s i l e m a te ria l i t is estim ated the United S ta te s ' sources o f econom ically recoverable f i s s i l e m a te ria l w ill be delin quished w ith in about tw e n ty -fiv e y e a rs J F is s ile m a te ria l can be produced w ith a breeder re a c to r. In a breeder re a c to r the f e r t i l e m a te ria ls U-238 and Th-232 are converted in to the f i s s i l e isotopes Pu-239 and U-233. The power use o f a breeder r e a c to r could in s u re our energy need f o r thousands o f years to come. In an e f f o r t to develop a breeder re a c to r the United States is fo rg in g ahead in the L iq u id Metal Fast Breeder Reactor (LMFBR) program. The LMFBR is a fa s t breeder re a c to r th a t u tiliz e s liq u id sodium as a c o o la n t. An im portant aspect o f the LMFBR program is the s a fe ty a n a lysis being conducted to determine the hazards and ris k s th a t accompany the wide spread use o f breeder re a c to rs. P ostulated accidents o f various 1

9 2 degrees o f s e v e rity are studied and analyzed to determ ine possible outcomes. The r e la tiv e p r o b a b ility o f the events which in i t i a t e such accidents could be examined in order to determ ine the p u b lic r is k. One class o f accidents which are o f very low p ro b a b ility is the h yp o th e tica l core d is ru p tiv e a ccid e n t (HCDA). Some o f the most severe o f the HCDA's r e s u lt in the gross d is ru p tio n and disassembly o f the core. In such an HCDA the extrem ely high vapor pressures cause an outward expansion o f the core m a te ria ls. Before an accid e n t in v o lv in g the disassem bly o f the core can occur, one must f i r s t p o s tu la te th a t a number o f very improbable i n it ia t in g events have taken place. In th is chain o f events i t is u s u a lly postula te d th a t there has been e ith e r a loss o f coola n t flo w, o r ramp in s e rtio n o f p o s itiv e r e a c tiv it y w ith f a ilu r e to scram. The r e a c tiv ity o f the system is a measure o f the net nuetron production r e la tiv e to th a t re q uire d to ju s t sustain the chain re a c tio n. F a ilu re to scram means th a t the backup and autom atic devices th a t have been engineered to provide a ra p id in s e rtio n o f negative r e a c tiv it y (such as the in s e rtio n o f c o n tro l rods) have not operated p ro p e rly. Under such c o n d itio n s, the core experiences very ra p id in te rn a l heating which could lead to the m e ltin g o f the core m a te ria ls. Fast reactors have the p ro p e rty th a t c e rta in lo c a l increases in the fu e l smeard e n s ity can lead to increases in the system r e a c tiv it y. In some 2 accid e n t scenarios th a t have been considered, molten fu e l can "slump" o r collapse in to such a re a c tiv e c o n fig u ra tio n. I f the r e a c tiv it y is increased w ith s u ffic ie n t speed, a ra th e r energetic a ccident would occur. Such an a ccid e n t would lead to the release

10 o f s u b s ta n tia l amounts o f energy and the d is p e rs a l o f the core to a s u b c r itic a l s ta te. The amount o f energy released and the consequent tem perature increases during such an accident provide the source terms f o r e v a lu a t ing the p o ssib le damage to.the prim ary system. The prim ary system c o n sists o f the elements th a t make up the closed loop co n ta in in g the liq u id sodium th a t a c tu a lly comes in c o n ta c t w ith the core. Such elements in clu d e the re a c to r v e s s e l, the p ip in g system, the pumps, and the steam generators. Extensive damage to the prim ary system could r e s u lt in the release o f ra d io a c tiv e m a te ria ls as w e ll as the h ig h ly chem ically re a c tiv e sodium. Thus i t becomes im portant to a c tu a lly c a lc u la te the mechanisms, such as the core expansion, which cause an a ccid e n t to shut-down and consequently lim its the amount o f energy th a t is released. One u s e fu l to o l which has been developed to account f o r these shut-down mechanisms as w e ll as c a lc u la te the energy release is a ra th e r com plicated computer program re fe rre d to as the VENUS-II 3 disassembly code. In the VENUS-II code, the various regions o f the re a c to r are tre a te d as a homogenous liq u id and the re s u ltin g hydro- dynamic equations are solved w ith numerical techniques. The basis f o r th is approach was o rg in a lly developed by Bethe and T a it.^ The vapor pressures, which a ct as the d riv in g fo rce s fo r the core expans io n, are ca lcu la te d using density-dependent e q u a tio n s -o f-s ta te. The block diagram found in Figure 1 gives one a s im p lifie d idea as to the process th a t is used to c a lc u la te the course o f the a ccid e n t. As one can see, there are two im porta n t feedback parameters th a t c o n tro l the

11 4 r e a c t iv it y o f the system. These are the displacem ent feedback and the Doppler feedback. The displacem ent feedback re s u lts from the m otion o f the re a c to r m a te ria ls which may cause the fu e l to assume a c o n fig u ra tio n th a t could increase o r decrease the r e a c t iv it y o f the system. For example, th e expansion o f th e core due to in te r n a l p re s sures would re s u lt in a negative r e a c t iv it y feedback. The Doppler feedback accounts fo r the r e a c t iv it y changes th a t occur in the temperatu re dependent p ro p e rtie s o f the re a c to r. T his is an im porta n t param eter in the fa s t re a c to r a ccid e n t a n a ly s is because th e re is a very d e fin ite negative r e a c t iv it y feedback th a t is associated w ith increased tem peratures. This can s ig n ific a n t ly reduce the consequences o f an a c c id e n t. Figure 1.. Block Diagram o f VENUS-II As in d ic a te d in th e above paragraphs, the d riv in g fo rc e fo r the core disassem bly was the vapor pressure o f the fu e l as c a lc u la te d by the e q u a tio n -o f-s ta te. E a rly stu d ie s in th is area d id not include

12 5 the a d d itio n a l pressures which can be produced by the fis s io n products th a t b u ild up in the fu e l. Recent stu d ies * *^* concern^ng the release and p re s s u riz a tio n o f the noble gases and o th e r fis s io n product vapor pressures have ind ica te d th a t the c o n trib u tio n o f these pressures may have a s ig n ific a n t a ffe c t on the core displacem ents in the e a rly stages o f the a ccid e n t. These a d d itio n a l d riv in g forces increase the outward a c c e le ra tio n o f the core m a te ria ls. This increases the negative r e a c tiv it y displacem ent feedback which in tu rn term inates the accident sooner. The net r e s u lt is to reduce the energy re le a se. One study has in d ic a te d th a t the energy release could be g reduced by as much as 80%. P re lim in a ry stu d ies concerning the e ffe c t th a t the fis s io n product p-'essures may have on the to ta l energy release in an HCDA, such as those examined by VENUS-II, d ic ta te d th a t an adequate fis s io n product pressure model be developed. The purpose o f th is work was to develop such a model, implement i t in to the VENUS-II disassembly code, and study the in flu e n c e th a t some o f the refinem ents would have on ty p ic a l disassembly c a lc u la tio n s. The improvements included in th is model should a llo w a more accurate and f le x ib le re p re se n ta tio n o f the fis s io n product p re s s u riz a tio n e ffe c ts.

13 CHAPTER I I PREDICTION OF THE EQUILIBRIUM PRESSURES As more com plicated and s o p h is tic a te d disassembly codes have been developed, i t has been apparent th a t the e ffe c ts o f the various fis s io n products should be inclu d ed. I t has not been obvious, however, as to p re c is e ly how th is should be done o r how they should be included. The com plicated behavior o f the fis s io n products and the la ck o f conclusive experim ental data made the problem a very d i f f i c u l t one to model on a sim ple b asis. A recent study by Brook sin g le d out some o f the physical and chemical p ro p e rtie s o f the fis s io n products th a t had an e ffe c t on the amount o f pressure they could c o n trib u te in the d is assembly process. Many o f the p re s s u riz a tio n parameters o f p o te n tia l s ig n ific a n c e required f o r an adequate fis s io n product pressure mode1 were defined by Brook. These.parameters w ill be discussed in more depth in the next s e c tio n. Another recent work by Gabelnick and Chasanov^ went to g re at lengths to p re d ic t the e q u ilib riu m vapor pressures o f the fis s io n products over a wide range o f v a ria b le s. Using the th e o re tic a l methods o f e q u ilib riu m thermodynamics they e xtra p o la te d the data a v a ila b le fo r the vapor pressures a t 2500 K up to tem peratures o f 6,000 K, which includes the normal range o f temperatures fo r ty p ic a l LMFBR disassembly c a lc u la tio n s. The a lg o rith m th a t they developed was based upon (a) "th e thermodynamic p ro p e rtie s o f th e condensed and vapor-phase fu e l and 6

14 7 fis s io n product species, (b) the mass c o n s tra in ts impossed by the fis s io n -p ro d u c t y ie ld s and release fa c to rs, the i n i t i a l fu e l compositio n, and the e x te n t o f fu e l burn-up, (the number o f fis s io n s th a t have taken place as compared to the to ta l fis s io n s p o s s ib le ) and (c) the re la tio n s h ip o f the oxygen p a r tia l pressure to the oxygen-to-m etal r a tio and plutonium fra c tio n o f the fu e l m a te r ia l." ^ By s o lv in g the re s u ltin g system o f simultaneous equations they c a lc u la te d the fis s io n product e q u ilib riu m pressures which were presented in ta b u la r form as a fu n c tio n o f the fu e l burn-up, fu e l sm ear-density, and tem perature. A sample o f t h is ta b u la te d data is given in Appendix A. In clu d in g th is a lg o rith m d ir e c t ly in VENUS-H would r e s u lt in a code th a t was unnecessarily bulky and long running. As an a lte r n a tiv e, i t was decided th a t curve f i t t i n g the various data p o in ts as presented by Gabelnick and Chasanov would provide a good basis fo r a fis s io n product model. Two reasons fo r using th e ir data are: l ) t h e ir work was the most extensive and accurate to date and 2) in a d d itio n to presenting the t o ta l vapor pressures o f the combined fu e l species and fis s io n p ro d u cts, they also presented the vapor pressures o f the a lk a li m etals, noble gasses, and fu e l species s e p a ra te ly. D iv id in g the pressures up in to the various groups gives g re a te r f l e x i b i l i t y to model the e ffe c ts th a t the d iffe r e n t fis s io n products may have on the o v e ra ll disassembly c a lc u la tio n s. The s im ila r it ie s in the p hysical and chemical p ro p e rtie s w ith in the groups make them re a c t s im ila r ly under the c o n d itio n s found in a nuclear re a c to r. Some o f the im porta n t physical e ffe c ts w ill be discussed in more d e ta il in the next s e c tio n.

15 8 To take advantage o f the grouped data as presented by Gabel n ick and Chasanov, i t was necessary to curve f i t th re e groups o f d a ta. Curve f i t t i n g these th re e sets separa te ly provided a set o f expressions fo r p re d ic tin g the a lk a li m etals vapor pressures, the noble gas pressures and the rem aining products vapor pressures se p a ra te ly. The remaining products vapor pressures consisted o f the ta b u la te d values o f the to ta l pressure minus the ta b u la te d values o f the a lk a li m etals, noble gases, and fu e l sp e cie s. A_. The Noble Gases Using the data from a s lig h t ly m odified ve rsio n o f Gabelnick and Chasanov s a lo g rith m and some thermodynamic co n sid e ra tio n s in v o lv in g g the theory o f corresponding s ta te s, Schwarzblat developed a n a ly tic a l expressions fo r the noble gases. Using c r it ic a l constants o f O gm/cm and 8190 K fo r the c r i t i c a l d e n s ity and tem perature, respect iv e ly, Schwarzblat obtained the fo llo w in g equation: PNG = B Tr/Vv where PNG = the pressure o f the noble gases (atm) B = the fu e l burnup in percent T r = the reduced tem perature (k) Vv = th e reduced v o id space volume The reduced value o f a p ro p e rty, such as tem perature o r volume, is the r a tio o f the absolute value o f the p ro perty to the value o f the prop e rty a t the c r i t i c a l p o in t. The reduced value o f a p ro p e rty is used in the theory o f corresponding sta te s and measures the d e v ia tio n o f the p ro perty from the c r i t i c a l p o in t. In the VENUS-II Code, the temperatures are stored as absolute tem peratures and the volumes are stored as reduced volumes. To make Schw arzblat1s equation com patible

16 9 w ith VENUS-II, his equation was d ivid e d by his c r it ic a l tem perature and d e n s ity so th a t the absolute tem peratures and volumes could be used. Then the equation was m u ltip lie d by the c r it ic a l d e n s ity used by VENUS-II, 3gm/cm3, so th a t the reduced volumes as ca lc u la te d by the code could be used. Then co n vertin g from atmospheres to dynes/cm^, the equation took the fo llo w in g form: PNG =2131 B T/Vv where PNG = pressures o f the noble gases (dynes/cm ^) B = burnup in percent T = tem perature (K) Vv = reduced v o id space volume EL The A1 kal i Metal s Using a le a s t squares curve f i t t i n g ro u tin e the a n a ly tic a l expressions f o r the a lk a li metals and the rem aining fis s io n products were obtained. The data p o in ts ta b u la te d by Gabel n ic k and Chasanov covered a tem perature range up to 6,000 K and were ta b u la ted fo r burn- ups o f 1,3,5, and 8 percent. To s im p lify the problem and o b ta in accurate f i t s over these ranges the data p o in ts were grouped and several d iffe r e n t piecewise expressions were used. This makes the p re senta tio n o f the e n tire set o f equations ra th e r bulky but presents no re a l problem f o r computer im plem entation. Sample equations fo r each group w ill be presented below and the e n tire set o f equations can be found in Appendix B. Both the a lk a li m etals and rem aining fis s io n products were f i r s t grouped according to the burnup. To a llo w fo r burnups other than those th a t were ta b u la te d, p ro v is io n s were included to provide lin e a r in t e r p o la tio n between 1 and 8 percent. Burnups o f less than 1 percent are

17 10 c u rre n tly not provided fo r in the model. Burnups g re a te r than 8 percent are rounded back to 8 percent p ro v id in g a co n serva tive estim ate o f the vapor pressure in th is re g io n. F urther s im p lific a tio n s were made by grouping the data according to tem perature. The a lk a li m etals were d iv id e d in to the fo llo w in g three tem perature ranges: less than 4,000 K, 4,000-5,000 K, and g re a te r than 5,000 K. Employing the piecewise equations over these three tem perature ranges provided an e x c e lle n t f i t to the data p o in ts. The expressions obtained f o r the vapor pressures o f the a lk a li metals a t a burnup on 3 percent are:. For tem peratures le s s than 4,000 K PAM = (3.654)D -(1.637)D 2+(.05549)D3 +(TX10"3 )( (3.669)D -(1.525)D 2+(.05836)D3) For tem peratures g re a te r than 4,000 K and le s s than 5,000 K PAM = (8.455)D +(6.84)D 2-( )D 3 +(TX10 3 ) ( ( )D -(l )D2+ ( )D3 ) For tem peratures g re a te r than 5,000 K Where PAM = (59.22)D -(4.691)D2+ (.l 499)D3 +(TX10-3 ) ( ( )D + (.7833)D2- ( )D3) PAM = Pressure o f th e a lk a l i m etals (atm) 3 D = Fuel smear d e n s ity gm/cm T = Temperature ( K)

18 11 C. The Remaining F ission Products The wide range o f physical and chemical p ro p e rtie s in th is group made a sim ple se t o f expressions more d i f f i c u l t to o b ta in. The 3 ta b u la ted d e n s itie s o f 3, 4, 5, 6, and 7 gm/cm had to be f i t t e d in d iv id u a lly w ith the lin e a r in te rp o la tio n between the d e n s itie s. Separate f i t s in the tem perature ranges were made fo r temperatures below 4500 K. and tem peratures above 4500 K. An expression f o r the 3 remaining products a t a burnup o f 3 percent and a d e n s ity o f 3 gm/cm are: where. L0G10PMP3= (.9501X10 4 )T +(.473X10 6 )T2 -(.5139X 10 10)T3 PMP3= Pressure o f the rem aining fis s io n products fo r a fu e l smear d e n s ity o f 3 gm/cm T= Temperature C K) (Atm) Figures 2 and 3 show the fa m ilie s o f curves th a t are generated by the a n a ly tic a l expressions w ith the data p o in ts superimposed fo r comparison. As these fig u re s show, even through data p o in ts were o n ly a v a ila b le up to 6000 K,the expressions were checked f o r e x tra p o la tio n s up to 10,000 K to make sure the re s u lta n t pressures appeared reasonable. The e x tra - 3 p o la tio n s fo r d e n s itie s between 1 and 10 gm/cm were also checked to 3 ensure reasonable re s u lts f o r any d e n s ity between 1 and 10 gm/cm. The re a de r is rem inded, however, th a t the accuracy o f the model f o r O tem peratures g re a te r than 6000 K and d e n s itie s g re a te r than 7 gm/cm are o n ly based on e x tra p o la tio n s due to the la ck o f data p o in ts in th is range.

19 Figure 2. Calculated Pressures of A lka li Metals fo r 3% Burnup

20 LOG,n (Pressure)(Atm ) F ig u re 3. C a lcu la te d Pressures o f the Remaining Products f o r 3% Burnup. CO

21 CHAPTER I I I RELEASE AND PRESSURIZATION PARAMETERS The behavior and in te ra c tio n o f the various fis s io n products before and during a prompt c r i t i c a l excursion is a su b je c t o f contin u ing study. That the fis s io n product vapor pressures a c tu a lly combine w ith the vapor pressure o f the fu e l species to increase the disassembly d riv in g fo rc e is w e ll e s ta b lis h e d. The e x te n t to which they in te r a c t, when-and how they are re le a se d, and the tim e scale req uire d fo r press u riz a tio n are im portant questions th a t have not y e t been f u l l y answered. The purpose o f th is th e s is is not to attem pt to resolve these questions but to provide a model th a t includes enough f l e x i b i l i t y to sim ulate a ll the mentioned a ffe c ts. With th is model one should be able to study the r e la tiv e importance o f the various release and press u riz a tio n parameters and determine the extend to which they a ffe c t the to ta l energy re le a se. This in fo rm a tio n can provide a basis fo r fu rth e r in v e s tig a tio n and research. When the behavior o f the fis s io n products is b e tte r determ ined, th is increased understanding can hopef u l l y be incorporated through proper choices o f the parameters included in the model. In the paragraphs th a t fo llo w, the release and p re s s u riz a tio n a ffe c ts which have been in v e s tig a te d w ill be discussed. I t w ill then be shown how p ro v is io n s were made in the fis s io n gas model to account fo r these various a ffe c ts. 14

22 15 A. S p a tia l R etention Modeling One o f the most im portant physical c h a ra c te ris tic s th a t must be accounted fo r is the s p a tia l d is tr ib u tio n and re te n tio n o f the various fis s io n products. Gabelnick and Chasonov assumed in th e ir a lg o rith m th a t 100% o f a ll the fis s io n products were re ta in e d w ith in the system ]^ In r e a lit y, a m ajor p o rtio n o f the fis s io n products have a ra th e r marked m o b ility w ith in the fu e l elements which allow s them to re lo c a te and/or escape from the fu e l. To account fo r th is m o b ility, s p a tia lly dependent re te n tio n fa c to rs were intro d u ce d. Separate re te n tio n fa c to rs fo r the a lk a li m e ta ls, noble gases, and the rem aining products provided the f l e x i b i l i t y to model the physical behavior associated w ith the m o b ility o f each group. Once the a p p ro p ria te re te n tio n fa c to r fo r each group has been determ ined, the pressures as p re d icte d by the a n a ly tic a l expressions are reduced by some fra c tio n to model the release o f the fis s io n products. The noble gases, f o r example, e x is t i n i t i a l l y as in d iv id u a l atoms w ith in the la t t ic e s tru c tu re o f the fu e l where they are formed through the fis s io n process. These in e r t gases, n o ta b ly xenon and kryp to n, are formed a t the ra te o f 0.26 atoms per f is s io n. 1^ Under steady s ta te opera tin g co n d itio n s some o f the noble gas atoms make th e ir way to the 12 g ra in boundaries by s in g le atom d iffu s io n. A t the g ra in boundaries and to some degree w ith in the la t t ic e s tru c tu re o f the fu e l the atoms c o lle c t to form small bubbles. The fu e l s tru c tu re o f an LMFBR co n sists o f a m a trix o f small c y lin d r ic a lly shaped ceramic (UO-) fu e l p in s. Each fu e l pin is encased by a th in s ta in le s s ste e l co n ta in e r. As shown in Figure 4, very steep

23 16 thermal g ra d ie n ts occur across the fu e l p in due to the poor thermal c o n d u c tiv ity o f the ceramic m a te ria l. In the c e n tra l p a rt o f the fu e l p in, th is tem perature g ra d ie n t imposed on the bubbles th a t have formed causes fu e l m a te ria l to be tra n s fe rre d from the hot face o f the bubble to the cold face by su b lim a tio n and subsequent condensating o f UC^ vapor. This a c tio n re s u lts in a net m otion o f the bubble up the th e r mal g ra d ie n t. The w id th o f the bubble d e fines the cross se ctio n o f the 13 columnar g ra in s tru c tu re th a t t r a i ls behind the moving bubble. Figure 5 illu s t r a t e s th e columnar s tru c tu re as formed by the moving bubbles. Figure Temperature D is trib u tio n in Fuel Pin As the bubbles c o lle c t a t the pin center a c e n tra l void region is created as shown in Figure 6. The flu c tu a tin g tem peratures th a t r e s u lt from v a ria tio n s in the power le v e l se t up la rg e stresses in the

24 17 Figure 5. Bubble T ra ils in Columnar Grains of Fuel Rod15

25 18 Figure 6. Irradiated Fuel Element Showing Central Void, Columnar Grain Growth, and Typical Reactor Startup and Shutdown Cracks Mag 23X17

26 19 p in s tru c tu re and cause extensive cra ckin g. The noble gases which have c o lle c te d in the p in center pass through these cracks to the gap th a t e x is ts between the fu e l and the cla d d in g. From here, the gases are c o lle c te d a t the upper end o f the fu e l pin in the fis s io n gas plenum, which is a c a v ity included f o r th is purpose. Near the o u te r ra d iu s in the c o o le r p a rts o f the p in, the fis s io n gases remained trapped in the fu e l m ic re s tru c tu re as in d iv id u a l atoms o r small bubbles and a t the g ra in boundaries in the form o f small bubbles. The decreased tem peratures in th is region decreases the gas m o b ility. Due to the s p a tia l dependence o f the neutron flu x d is tr ib u tio n in a re a c to r, the tem peratures near the end o f the pins are also s ig n ific a n t ly low er. These low er tem peratures also re ta rd the bubble m ig ra tio n and lead to a g re a te r re te n tio n o f the noble gases near the pin ends c re a tin g a need f o r the s p a tia lly dependent re te n tio n fa c to rs. The use o f mesh c e lls in the VENUS-II disassem bly code to represent the various p a rts o f the reaccor core e lim in a te s the ra d ia l e ffe c ts (w ith in a p in ) o f the noble gases re te n tio n and o n ly allow s fo r changes th a t occur a x ia lly. The mesh c e ll represents an area th a t would inclu d e several diam eters o f the fu e l pins but o nly a fra c tio n o f the to ta l length o f a fu e l p in. Due to th is lim it a t io n, a onedimensional re te n tio n fa c to r was esta b lish e d which depended o n ly on the distance from the pin cente r in the a x ia l d ire c tio n. In the case o f the a lk a li m etals (which do not appear in a gaseous phase but in a s o lid phase) an e n tir e ly d iffe r e n t physical behavior is observed. Rather than m ig ra tin g up the thermal g ra d ie n t, the a lk a li m etals, such as cesium and rubidium, tend to m igrate down

27 20 the thermal g ra d ie n t to the ends and o u te r surfaces o f the f u e l. 6 Lambert e t al have measured the lo c a l concentrations o f the cesium in fu e l pins th a t were irra d ia te d in Experimental Breeder R e a c t o r - I lj 6 Localized co n centra tio n peaks were measured in the gap between the fu e l p e lle ts and the c la d d in g. the ends o f the fu e l p in s. Peak concentra tio n s were also measured near Brook has pointed o u t th a t the concentratio n s o f the cesium near the ends o f the pins may c o n trib u te s i g n i f i c a n tly in the pressure forces in th a t region which may oppose the core expansion and slow down the a c c id e n t shutdown mechanism. The d iffe re n c e s in the behavior o f the a lk a li m etals and the noble gases accounts fo r the necessity o f p ro vid in g separate re te n tio n fa c to rs in modeling the re te n tio n o f fis s io n products w ith in the fu e l. I t was decided th a t a second-order equation th a t u tiliz e d the a x ia l p o s itio n as the independent v a ria b le and th a t could be symmetrical about any a x ia l p o s itio n would provide adequate f l e x i b i l i t y to model a v a rie ty o f a x ia lly dependent re te n tio n fa c to rs. Figure 7 illu s tr a te s a few o f the re te n tio n p r o file s th a t the model can accommodate. The v e r tic a l a xis represents the fr a c tio n o f the fis s io n products re ta in e d. The h o riz o n ta l a xis represents the a x ia l p o s itio n w ith zero being the bottom o f the re a c to r core and one being the to p. Due to the fa c t th a t the fis s io n product m ig ra tio n is h ig h ly dependent on the fu e l tem perature, the shape o f the re te n tio n p r o file s may be q u ite s im ila r to the tem perature p r o file s. Figures 7a and 7b demonstrate how the re te n tio n p r o file could be skewed toward the top o r bottom o f the re a c to r. Other constant and lin e a r ly dependent re te n tio n fa c to rs th a t can be modeled are shown in fig u re s 7c and 7d re s p e c tiv e ly.

28 21 F ig u re 7. A Sample o f the Various R etention P r o file s th a t can be Obtained w ith the F is s io n Product Pressure Model.

29 22 To o b ta in the re te n tio n p r o file s shown in fig u re 7, the VENUS-II user is require d to p ro vid e fiv e parameters fo r each o f the three fis s io n product groups, o r a to ta l o f fifte e n parameters,. The f i r s t three parameters f i x a c e n tra l lo c a tio n about which the re te n tio n prof i l e is symmetrical and the rem aining parameters are used to determine the c o e ffic ie n ts o f a second o rd e r equation. To determ ine the parameters required to achieve a desired outcome, the user should fo llo w the fo llo w in g steps: 1. Determine the lo c a tio n in the core where the minimum re te n tio n occurs (o r in o th e r words the a x ia l lo c a tio n where the maximum fis s io n product release has o ccurre d ). T h is sh a ll be re fe rre d to as the center p o s itio n. The lo c a tio n o f the cente r p o s itio n should be determined and expressed as the number o f nodes or fra c tio n o f nodes between the base o f the re a c to r, in c lu d in g the b lanket re g io n, and the center p o s itio n. 2. Determine the number o f nodes, o r fra c tio n o f nodes, from the cente r p o s itio n to the most d is ta n t b la n ke t/core in te rfa c e (where the fu e le d core region ends and the b la n ket region begins). 3. Determine what is considered the best estim ate o f the fr a c tio n o f the fis s io n products re ta in e d a t the cente r p o s itio n, a t the core in te rfa c e discussed in step 2, and a t a p o in t midway between these two p o in ts. Using the three estim ates from step th re e, the code derives the three c o e ffic ie n ts o f a second order equation th a t w ill g ive the re te n tio n a t the s p e c ifie d p o in ts using the fo llo w in g equations: B1 = -4.0 (RET2-.5RET1-.5RET3) B2 = -RET3-RET1+2RET2 B3 = RET1 where RET1 = The fr a c tio n a l re te n tio n a t the cente r p o s itio n.

30 23 RET2 = The fra c tio n a l re te n tio n a t a p o in t midway between the cente r p o s itio n and the c o re /b la n k e t in te rfa c e. RET3 = The fra c tio n a l re te n tio n a t the c o re /b la n k e t in te rfa c e. E s s e n tia lly these equations represent the s o lu tio n to three sim ulta n eous equations which are obtained by using the three user s p e c ifie d re te n tio n fa c to rs. Using the a x ia l lo c a tio n o f a node r e la tiv e to the center p o s itio n, and the c a lc u la te d c o e ffic ie n ts, a fra c tio n a l re te n tio n fa c to r is determined f o r th a t node from th is equation: where FRF = B1CX2) + B2(X) + B3 X = the r e la tiv e lo c a tio n o f the node FRF = fr a c tio n a l re te n tio n fa c to r This fra c tio n a l re te n tio n fa c to r is used to reduce lo ca l c o n trib u tio n s o f the pressure associated w ith th a t group. This reduces the pressures as p re d icte d by Gabel n ic k and Chasanov to account fo r release o f the various fis s io n products. j j. P re ssu riza tio n Under T ra n sie n t C onditions The preceeding se ctio n e xplains how the d is tr ib u tio n o f the fis s io n products p r io r to a prompt c r i t i c a l excursion is accounted fo r in the fis s io n product pressure model. During the i n i t i a l stages o f an e xcursio n, the fis s io n products are in the form o f small bubbles w ith in the s o lid la t t ic e s tru c tu re s o f the fu e l. I t is possib le th a t w ith in m illis e c o n d s a fte r the in it ia t io n o f such an excursion the fu e l has melted g iv in g more freedom to the small bubbles. This would a llo w them to coalesce and e ffe c tiv e ly p re s s u riz e. The delay tim e associated

31 24 w ith th is p re s s u riz a tio n can be g re a tly a ffe c te d by such th in g s as the bubble s iz e. The surface tension associated w ith the s m a lle r bubble sizes could s ig n ific a n t ly re ta rd the bubble growth i f the fu e l suddenly becomes m olten. The temperatures and co n d itio n s associated w ith th is p re s s u riz a tio n ra te makes i t d i f f i c u l t to gain much in s ig h t in the form o f experim ental data. Thus, p re d ic tin g the behavior o f the fis s io n products under these c o n d itio n s is a d i f f i c u l t problem. Studies in th is area have in d ic a te d some o f the phenomena th a t should be taken in to c o n s id e ra tio n. G ru b e r^ has suggested th a t during the severe tra n s ie n ts in which gross m e ltin g o f the fu e l occurs there are several p o s s ib ilitie s to consider w ith regard to the subsequent fis s io n product p re s s u riz a tio n. " F ir s t the small bubbles may be swept along the phase boundary, le a d in g to enhanced coalescence. N ext, the in te rlin k e d p o ro s ity on the g ra in boundaries and g ra in edges (th a t are formed during the m ig ra tio n o f the bubbles and the fu e l re s tru c tin g under steady s ta te operating c o n d itio n s ) may be expected to close up again in to s p e ric a l pores, tra p p in g the re sid u a l gas. Because o f the volume increase associated w ith the m e ltin g, the h y d ro s ta tic pressure w ill a lso increase, keeping the bubbles sm all. These small bubbles w ill be h ig h ly m obile and coalescence on a very s h o rt time scale may r e s u lt. Enlargement o f the bubbles can occur by viscous flo w, and there may be s ig n ific a n t c o n trib u tio n o f the gas to the h y d ro s ta tic pressure in the liq u id f u e l. " ^ E s s e n tia lly then, there are two mechanisms which must be accounted fo r in modeling the p re s s u riz a tio n ra te o f the fis s io n products under tra n s ie n t c o n d itio n s : 1) a release o r i n it ia t io n mechanism th a t allow s the bubble to fre e ly coalesce (such as the m e ltin g o f the

32 25 fu e l). 2) A delay tim e o r a p re s s u riz a tio n tim e from the tim e they are released to the tim e they are f u l l y p re ssurized. V arious atte m p ts have been made to model the re le a s e and p re s s u riz a tio n o f the fis s io n products. A sim ple approach used by General E le c tric in a code c a lle d T ra n sie n t Overpower Fuel F a ilu re (TOFF) assumes th a t the bubbles become a fr e e ly com pressible f lu id th a t w ill 1 g h y d ro s ta tic a lly p re ssurize the core when the fu e l becomes m olten. This model accounts fo r the release o f the fis s io n products but p ro vides no time delay f o r p re s s u riz a tio n. Another release model proposed by Brook assumes th a t the fis s io n products are released as the m elt fr o n t proceeds from the c e n te r o f the pin to the o u te r ra d iu s To accomplish th is he assumes th a t the m e lt fr o n t proceeds lin e a r ly w ith an increase in the mean fu e l temperature from KJ6 The actual m e ltin g tem perature o f the ceramic fu e l m a te ria l is estim ated to be 3040 K. Although th is may be an improvement over the General E le c tric model i t s t i l l does not provide a means to vary the p re s s u riz a tio n ra te to model the tim e scale as suggested by Gruber A very re ce nt study by Eaton 5 included some p ro v is io n s fo r tim e de la y in a model th a t he proposed f o r use in the VENUS-II code. His model releases a ll o f the fis s io n products by using a s in g le temperature c r ite r io n. Once the p reset temperature has been reached, a separate time m a trix is used to keep tra c k o f the tim e as i t marches forw ard. When the tim e delay fo r a p a r tic u la r group has been exceeded, the pressure a s so cia te d w ith the group is summed w ith the vapor p re s sure o f the fu e l. The tim e m a trix allow s the advance o f tim e to be clocked fo r each in d iv id u a l mesh c e ll found in the VENUS-II code. A drawback o f th is model is th a t i t d id not a llo w the d iffe r e n t products

33 26 to be released a t d if fe r e n t tem peratures but assumed th a t a s in g le in it ia t io n tem perature was s u ffic ie n t. The fis s io n product p re s s u riz a tio n model presented here provides the user w ith enough in p u t parameters to a llo w fo r a v a rie ty o f p re s s u riz a tio n ra te s. The i n i t i a l release o f the fis s io n products is accomplished w ith a tem perature c r ite r io n. By supplying three d iffe r e n t release temperatures corresponding to the a lk a li m etals, noble gases and the rem aining fis s io n products the p re s s u riz a tio n e ffe c t o f each group is in it ia t e d. Once the in d ic a te d tem perature fo r a p a r tic u la r mesh c e ll has been reached fo r a s p e c ifie d fis s io n product group the to ta l tim e from the in it ia t io n o f th a t group is accounted fo r. This tim e becomes an e ffe c tiv e tim e r fo r varying the p re s s u riz a tio n ra te associated w ith each o f the groups. A llo w in g fo r the separate i n i t i a t i o n, or re le a se, o f the three groups is an im portant improvement th a t th is new model provides,, In the case o f the a lk a li m etals, fo r example, a much lower tem perature may be a p p ro p ria te. Due to the fa c t th a t the a lk a li m etals have lo c a l co n centra tio n peaks a t the fu e l surface i t may not be necessary fo r the fu e l to reach a molten s ta te before the a lk a li m etals p re s s u riz e. Since the a lk a li m etals e x is t in elemental form a t the fu e l surface there are no bubbles o r surface tension e ffe c ts to overcome and they sim ply need to evaporate to produce a vapor pressure. T his would a llo w the a lk a li m etals to e ffe c tiv e ly c o n trib u te to the system pressure a t a much lower tem perature. To enable the user to c o n tro l the p re s s u riz a tio n tim e th a t each group experiences a fte r i t has been in it ia t e d, two more parameters are re q uire d fo r each o f the three groups. F ir s t an absolute delay time

34 27 Is re q u ire d. During th is delay tim e i t is assumed th a t the fis s io n product being considered w ill not make any s ig n ific a n t c o n trib u tio n to the m esh-cell pressure. Once the delay tim e has been exceeded fo r any p a r tic u la r fis s io n product group (a t any p a r tic u la r node) the fis s io n products are allow ed to e x p o n e n tia lly p re s s u riz e. By supplying the tim e constant associated w ith th is exponential ris e the user can model a wide v a rie ty o f p re s s u riz a tio n ra te s. With th is model, the pressure continues to ris e approaching the pressure th a t has been c a lc u la te d from the a p p ro p ria te a n a ly tic a l equations and th a t has been p ro p e rly reduced to account fo r the release o f th a t product under steady s ta te operating co n ditio n,, Figure 8 in d ic a te s a few o f the p re s s u riz a tio n ra te s th a t could be u tiliz e d in modeling the fis s io n product p re s s u riz a tio n. The equation governing the exponential press u riz a tio n i f where FPR = 1-EXP(TCRT-DT)/TAU) FPR = The fr a c tio n re d u ctio n fa c to r due to the p re s s u riz a tio n ra te TCRT = The absolute delay tim e DT = Time progressed since the p re s s u riz a tio n in it ia t io n TAU = Time constant associated w ith the p re s s u riz a tio n ra te. The most s ig n ific a n t fis s io n product group in terms o f the pressure th a t i t can c o n trib u te is the noble gas group. A d d itio n a l f l e x i b i l i t y is provided in modeling the p re s s u riz a tio n ra te o f th is group by d iv id in g the pressure in to th re e fr a c tio n s Each fra c tio n o f the pressure is then assigned a delay tim e and a time constant as

35 Pressure (atm) Figure 8. Pressurization Rates with D ifferent Delay Time.

36 29 explained above. By a d ju s tin g the fra c tio n sizes the user can c o n tro l when and to what degree the fis s io n products are p re s s u riz in g. Thus, i f a fra c tio n o f the noble gases are thought to p re ssurize e a rly (due to t h e ir bubble size or p hysical lo c a tio n w ith in the fu e l) and another fr a c tio n p ressurizes a t a le te r tim e the model would be f le x ib le enough to handle the s itu a tio n. Appendix C contains a d d itio n a l in fo rm a tio n concerning the use o f th is improved fis s io n product pressure model in the VENUS-II d is assemble code Provided in the appendix is a l i s t o f the parameters th a t the user must supply, the F o rtra n form at statements fo r reading them- in, and a sh o rt statem ent concerning the fu n c tio n o f each parameter. Also supplied in the appendix is a lis t in g o f the equation o f s ta te subroutine where the fis s io n product pressure model was in serted and a flo w c h a rt showing the lo g ic used in a d ju s tin g the fis s io n product pressures to account fo r the fis s io n product release and press u riz a tio n ra te s.

37 CHAPTER IV THE EFFECTS OF THE FISSION PRODUCT PRESSURES IN SAMPLE DIASSEMBLY CASES To make sure th a t the model was fu n c tio n in g as desired and to perform an i n i t i a l s e n s it iv ity stu d y, several te s t cases were run using the fis s io n gas model. The re s u lts o f th is study w ill be presented in th is chapter. A base case was e sta b lish e d in which the fis s io n product pressures were not inclu d ed. Using th is as the base fo r comparison o th e r cases were run which u tiliz e d the various c a p a b ilitie s o f the new fis s io n product pressure model. A burnup o f fiv e percent (5%) was used in each o f th e te s t cases. In the f i r s t three cases, the r e la tiv e incluence o f the th re e fis s io n product groups was determ ined. In the f i r s t case (case 1) the noble gases were considered alone. In the second case (case 2) the e ffe c ts o f the noble gases and the rem aining products were considered. The th ir d case (case 3) included a ll three fis s io n product groups, i. e. the noble gases, the a lk a li m etals, and the rem aining fis s io n products. In each case a constant a x ia l re te n tio n o f 0.10 was assumed fo r each group being considered. When a group was not being considered the a x ia l r e te n tio n s were s e t to ze ro. The purpose o f these cases was to demons tra te the r e la tiv e importance o f each o f the fis s io n product groups in a ty p ic a l disassembly c a lc u la tio n. For s im p lic ity in comparing these 30

38 31 r e s u lts, th e fis s io n product pressures were insta nta n e o u sly in it ia t e d upon fu e l m e ltin g a t a tem perature o f K. The comparison o f the d iffe r e n t cases was based on the to ta l energy release and the negative displacem ent r e a c tiv it y. Thus the changes in the displacem ent r e a c tiv it y could be monitored w ith each tim e step to see how the changes in the fis s io n product pressures a ffe c te d th is im porta n t shutdown mechanism. These flu c tu a tio n s in the displacem ent r e a c tiv it y in tu rn a ffe c te d the energy release during the a ccid e n t. The energy release was also m onitored w ith each tim e ste p. Figure 9 and 10 demonstrate how the to ta l energy release and the negative displacem ent r e a c tiv it y varie d fo r the f i r s t three cases as a fu n c tio n o f tim e. The energy release and the displacem ent r e a c tiv it y o f the base case are a lso included f o r comparison. As fig u re s 9 and 10 c le a rly in d ic a te, the noble gases are the most s ig n ific a n t pressure source. In fig u re 9 one can see th a t the in c lu s io n o f the noble gas pressures reduces the energy o u tp u t o f the a ccid e n t by 58% w h ile in c lu d in g the o th e r two groups o n ly reduced the energy o utput by an a d d itio n a l 9%. Figure 10 illu s t r a t e s the changes th a t occur in the displacem ent r e a c tiv it y. The negative r e a c tiv it ie s in fig u re 10 u ltim a te ly d riv e the system s u b c ritic a l and te rm inate the power b u rs ts. The shutdown o f the a ccid e n t can be detected in fig u re 9 as the p o in t where the energy releases become constant. I t is in te re s tin g to note in fig u re 9 th a t the energy release fo r any case is n e a rly equal during the f i r s t stages o f the a ccid e n t. Two reasons suggested fo r th is behavior a re : (1) the in e r tia o f the core re s is ts expansion and causes a delay in the negative displacem ent r e a c tiv it y u n til the core can a c tu a lly be accelerated and moved to any

39 Energy (MW-Sec X 10 F ig u re 9. T o ta l Energy Release as a Function o f Time. CO ro

40 Displacement R e a c tiv ity ($) Figure lq. Time (m illis e c o n d s ) Displacem ent R e a c tiv ity as a Function o f Time. CO CO

41 34 degree, and ( 2 ) as higher tem peratures are achieved throughout the core the magnitude o f the fis s io n product pressures also increase. Once the in e r t ia o f the system has been overcome and the tem peratures in the core are high enough to generate a s ig n ific a n t amount o f fis s io n product pressures, the energy release is decreased and the a ccid e n t is term inated. In ta b le 1, the energy release a tta in e d in the f in a l tim e step has been normalized fo r each case. The energy released in the base case was se t equal to 1 and the energy release o f the remaining cases expressed as a fra c tio n o f the base case. Here again the s ig n ific a n c e o f the noble gases are apparent when one compares the energy released in cases 1, 2, and 3. The next case (.case 4) in v e s tig a te d the possib le a ffe c ts o f co n centra tin g a p o rtio n o f the fis s io n products a t the top and bottom o f the re a c to r. As in the previous cases the p re s s u riz a tio n was assumed to be instantaneous upon the m e ltin g o f the fu e l. By choosing to e s ta b lis h an average re te n tio n o f the to ta l re te n tio n in th is case would be the same as the to ta l re te n tio n in case 3. This would p erm it a s tr a ig h t forw ard comparison to be made between case 3 and case 4. An average re te n tio n o f 0.10 was obtained by s p e c ify in g re te n tio n fa c to rs o f 0.02, , and 0.23 as in p u t to the code. These in p u t parameters re s u lte d in the fo llo w in g equation FRF = 0.1 5(X2 ) (X) where FRF = fra c tio n a l re te n tio n fa c to r. X = r e la tiv e a x ia l lo c a tio n o f node.

42 35 Table 1. Summary o f F ission Product Pressure A ffe c ts o r Energy Release fo r Disassembly C a lc u la tio n s. CASE # RELATIVE ENERGY RELEASE CASE # RELATIVE ENERGY RELEASE BASE E 4.65E 1 c n 00 m 5. 63E 2. 55E 6 CO U J 3.49E

43 36 This equation was then used to determ ine the a x ia l release o f the fis s io n products o f a ll three groups. I t can be demonstrated th a t the average re te n tio n here is equal to 0.10 by in te g ra tin g the above e q ua tio n from zero to one. Figures 11 and 12 compare the energy release and the negative displacem ent r e a c tiv it y fo r case 3 and case 4. The in fo rm a tio n on th e base case is again in c lu d e d f o r com parison. By examining ta b le 1 and fig u re 11 one can see th a t the energy release is increased by 16% over the base case. As would be expected, the negative displacem ent r e a c tiv it y was delayed in making any s ig n ific a n t in s e rtio n o f negative r e a c t iv it y as shown in fig u re 12. There are two possib le explanations fo r these re s u lts. F ir s t, as was suggested by Brook6, the concentratio n o f the fis s io n products near the top and bottom o f the core could create pressures th a t oppose the core expansion. This lim its the amount o f negative r e a c tiv it y in s e rte d and increase the d u ra tio n and energy o u tp u t o f the a ccid e n t. A second e xplanation takes in to account the tem peratures o f the va rio u s regions. Instead o f being evenly d is trib u te d along the length o f the core the fis s io n products are now locate d near the ends o f the re a c to r where the temperatures are s ig n ific a n t ly low er. The i n i t i a l co n d itio n s o f th is accident a n a ly s is are such th a t the ce n tra l p o rtio n o f the re a c to r has already exceeded the m e ltin g tem perature. This means th a t s ig n ific a n t pressures can be generated by the fis s io n products from the i n it ia t io n o f the a ccid e n t in case 3. A s h if t in the d is tr ib u tio n o f the fis s io n products o f the c o o le r regions o f the core in case 4 re s u lte d in s ig n ific a n t delays u n til the tem peratures

44 Figure 11. T o ta l Energy Release as a Function o f Time.

45 Displacement R e a c tiv ity ($) Figure 12. Time (m illis e c o n d s ) D isplacem ent R e a c tiv ity as a Function o f Time. U> 00

46 39 In th a t region were high enough to cause the fis s io n products to p re s s u riz e. This la t t e r e ffe c t is probably the dominant in incre a sing the energy re le a se. The two fin a l cases, cases 5 and 6, in v e s tig a te the e ffe c ts o f delaying the p re s s u riz a tio n o f the noble gases. By c a r e fu lly choosing the delay time param eters, i t was hoped th a t lim itin g cases could be e s ta b lis h e d. A constant a x ia l re te n tio n o f 0.10 was used in each case and the o p tio n o f d iv id in g the noble gases in to th re e groups was used to delay the p re s s u riz a tio n o f the re s u lta n t pressures. By choosing a constant re te n tio n o f 0.10, the re s u lts o f case 1 could be used in the comparison. I t would a c t as a lim itin g case by a llo w in g the noble gases to p re ssurize in sta n ta n e o u sly upon the m e ltin g fo the fu e l. In case 5 the noble gases were d ivid e d in to two groups, group one accounted f o r 20% o f the noble gases and group two accounted fo r 80%. A delay time o f 0.5 seconds was a pplied to group one and group two was allowed to p re ssurize in s ta n ta n e io u s ly when the in it ia t io n tem perature was reached. In th is case the percentages on the two groups were interchanged. This meant th a t o n ly 20% o f the noble gas pressures would be a v a ila b le in the e a rly stages o f the disassem bly w h ile 80% would be so delayed in p re s s u riz in g th a t the a ccid e n t would be e s s e n tia lly over before i t make any c o n trib u tio n. Figure 13 compares the energy released in cases 1, 5, 6, and the bases case. As one m ight suspect the energy release was almost p ro p o rtio n a l to the fr a c tio n o f the pressure th a t was released w ith the m e ltin g o f the fu e l. In cases 5 and 6 the energy release increased o ver th e energy re le a se in case 1 in an amount th a t was alm ost

47 Energy (MW-Sec X 10 Figure 13. T o ta l Energy Release as a Function o f Time. o

48 41 p ro p o rtio n a l to the amount o f the noble gases th a t were allowed to p re ssurize in the e a rly stages o f the a ccid e n t. In examining the re s u lts shown in fig u re 14, which shows the negative displacem ent r e a c tiv it y f o r cases 1, 5, 6, and the base case, the re s u lts are much the way one would expect them to be except fo r one fa c t. The displacem ent r e a c t iv it y o f the base c a s e 'a c tu a lly exceeds the displacem ent r e a c tiv it y o f case 6 a fte r a c e rta in p o in t in tim e. The slope o f the lin e in d ic a tin g the displacem ent r e a c tiv it y o f the base in d ic a te s a very ra p id change in the displacem ent r e a c tiv it y. This could be caused by the fa c t th a t in the absence o f the fis s io n products, the accid e n t has progressed s ig n ific a n t ly fu rth e r and re s u lte d in higher tem peratures. These higher tem peratures cause a very ra p id and extensive p re s s u riz a tio n in the form o f fu e l vapor pressure. The high a c c e le ra tio n s encountered under such p re s s u riz a tio n r e s u lt in higher v e lo c itie s which tends to d is ru p t the core very q u ic k ly. On the other hand, the pressures o f the noble gases which are encountered very e a rly in the disassembly stages o f case 6 s ig n ific a n t ly re ta rd s the n e u tro n ic a c t iv it y which in tu rn slows down the ra te o f tem perature increase. This re s u lts in a slower p re s s u riz a tio n and hence sm a lle r a c c e le ra tio n s and low er v e lo c itie s. Hence the displacem ent r e a c tiv it y o f the base cases can a c tu a lly exceeds th a t o f case 6. S im ila rly the slope o f the displacem ent r e a c tiv it y curves in cases 1 and 5 are s ig n ific a n t ly less than th a t o f the base case.

49 Displacement R e a c tiv ity ($) Figure 14. Displacement R e a c tiv ity as a Function o f Time. - t * r>o

50 CHAPTER V SUMMARY AND CONCLUSIONS In the search fo r clean, safe and long-term energy every source should be c a r e fu lly considered. Studies such as the one done in th is th e s is should continue to provide a d d itio n a l in fo rm a tio n and b e tte r to o ls to aid in understanding o f breeder re a c to r s a fe ty. The fis s io n product pressure moded presented in th is paper should become an im porta n t to o l in e va lu a tin g the re s u lts o f h yp o th e tica l core d is ru p tiv e a ccid e n ts. As the s e n s it iv ity study in d ic a te d, an in c lu s io n o f the pressures generated by re ta in in g o n ly 10% o f the fis s io n products reduced the energy release by about 50%. Should fu tu re stu d ie s in d ic ate an even higher re te n tio n o f the fis s io n products w ith the la t t ic e s tru c tu re o f the fu e l, th is energy re d u ctio n could become even more s ig n ific a n t. Should the use o f th is model become widespread enough to re q u ire more re fin em e n ts, the author suggests th a t improvements be made in supplying the i n i t i a l c o n d itio n s o f the accid e n t fo r the fis s io n product pressure model. In many cases the m e ltin g tem perature o f the fu e l has already been exceeded near the core cente r. Yet as the model now fu n c tio n s even in these regions the p re s s u riz a tio n o f the fis s io n products must w a it u n til the delay tim e has been exceeded. One s o lu tio n to th e problem would be to read in an a rra y o f data th a t would 43

51 44 in d ic a te the amount o f tim e th a t each mesh c e ll has spent above the m e ltin g tem perature o f the fu e l.

52 APPENDIX A Sample o f Tabulated Data as Presented by Gabel n ic k and Chasanov. 45

53 46 Table 2 is a sample o f the ta b u la ted data p o in ts th a t were presented by Gabel n ick and C hasanov.^ Tables were presented th a t lis t e d data p o in ts fo r burnups 1,3,5 and 8%. The data lis t e d in Table 2 is fo r a burnup o f 3%. This data represents the e q u ilib riu m vapor pressure o f the d iffe r e n t fis s io n product groups c a lc u la te d using the a lg o rith m developed by Gabel n ic k and Chasanov. The pressure o f the rem aining fis s io n products can be determined by s u b tra c tin g the pressure o f the noble gases, the a lk a li m etals, and the fu e l species from the to ta l pressure.

54 APPENDIX B T abulation o f A n a ly tic a l Expressions f o r the Pressures o f the A lk a li M etals and the Noble Gases. 48

55 49 The fo llo w in g a n a ly tic a l expressions, p re d ic t th e e q u ilib riu m pressures o f the a lk a li m etals and the rem aining fis s io n products. Accurate f i t s to the data c a lc u la te d by G abelnick and Chasanov were obtained by grouping the data according to burnup, tem perature and fuel-sm ear d e n sity and using a le a s t squares f i t t i n g ro u tin e to fin d the c o e ffic ie n ts to a polynomial e q uatio n, the equations are w ritte n in F o rtra n Language. The f i r s t group o f equations are the a n a ly tic a l expressions fo r the e q u ilib riu m vapor pressure o f the rem aining products. KET: The d ig i t a fte r the PMP in d ic a te d the fu e l smear d e n s itie s. For example PMP3 is the e q u ilib r iu m vapor pressure o f the 3 remaining fis s io n products fo r a fu e l smear d e n s ity o f 3 GM/CM.

56 50 PRESSURE OF THE REMAINING PRODUCTS FDR BURNUP OF 3X FOR TEMPERATURES LESS THAN 4500 DEG K PMPl«-2.47b *T+.39bE-06*T**2-.«25PE-10*T**3 PMP2» l4?E-03*T+.3bllE-0b*T**2-.421E-10*T**3 PMP3»-2, E-04*T+.4730E-0fe*T** E-10*T**3 PMP4»-?,U0fj-,54 99E-0<t*T E-06*T«* SE-10*T**3 PMP5»-2, E-03*T+.24!bE-0b*T**2-.2blBE-10*T**3 PMP6» * E-03*T^. 1354E-06*T**2-.88«1E-11 *T**3 PMP7» E-03*T+. 173BE-0b*T** E-1 0*T**3 PMP83.3> E-03*T+.fc973E-07AT** E-12<rT-*i*3 PMP9*.3594+,288E-03*T+.4733E-07*T** E-12*T**3 PMPl0a, E-03<*T +,fa520e-07*t**2.2416e-ll«t**3 FOR TEMPERATURES GREATER THAN 4500 DEG K PMPl -2, *T-.5172E-06*T**2+,5719E-10*T**3 PMP2o B02B7B*T-.B051E-06»T**2+.B98BE-10*T«*3 PMP3=-2.2Ub+.2339E-02*1-.b99iE-0b*T** E-10*T**3 PMPOa bB8E-02*T-. le83e-05*t**2f.116be-09*t**3 PMP5= E-02*T-.8235E-0b*T**2+,9485E-10*T**3 PMPb= E-02* E-0b*T**2+.88B5E-10*T**3 PMP7=-1.77b+.2175E-02*T-.5805E-0b*l**2+.fc532E-10*7**3 PMP8» Rlb21*T-.3S4iE-0b«T**2+,45IE-10*T**3 PMP9x-.59l5^.n0lE-02*T-.20b2E-0fe.T** E-l0*T**3 PMPl0«-t bE-03*T-.B448E-07*T**2+,1451E-10*Tn.*3

57 PRESSURE OF THE REMAINING PRODUCTS FOR BURNUP OF 1* FOR TEMPERATURES LESS THAN 0500 DEG K PMPla3,803-.0a38fe?*T+.1195E-05*T** E-09*T**3 PMP2= *T+.5839E-0b*T** E-10*T**3 PMP3=-1.35B+,993bE-03+T-.2O84E-0b+T+*2+.3bbaE-10*T+*3 PMPO S5*T-.54B3E-0fe*Ti**2 +.fe7 8flE-10*T**3 PMP5» E-02*T-.7033E-0fe*T**2+.83fe5Er 10*T**3 PMPb=-2, b0E-0?*T-.Bb42E-0b*T**2+.977bE-10*T+*3 PMP7*-2.fc8b+.002b76*T-.734bE-0b*T**2+,819E-10*T**3 PMP *T-.502OE-0b+T** E-10*T+*3 PMP b5*T-.33b8E-06*T+* E-10*T**3 PMP ,001926*T-.5042E-0fenT*A E-10*T**3 FOR TEMPERATURES GREATER THAN 4500 DEG K PMPlr-i E-03 + T+. 128BE-06*T* * E-10*J**3 PMP2s-2,P E-03*T+.2«73E-06*T**2'-.2589E-10*T**? PMP3=-2, E-03*T+.«203E-06*T** E-10*T**3 PMP4= E-03*T+.3384E-06*T**2-.fl05E-10*T*+3 PMP5x-3,006+.'l 432E-03*T+.3957E-06*T** E-10.T**3 PMP6 = b4bt-0<i*T +.315E-06*T + *2-.31fl4E-10*T*.*3 PMP7a-l,05b+.2405E-03*T+.147bE-0bi*T + *?-.1180E-l0*T**3 PMP8 = 1,03b E-0O + T E-07*T * i* E-1 l*x+ *3- PMP9a-3,298+,00208b*T-.2521E-0b*T* E-10*T**3 PMPl0r.6b E-03*T-.6b08E-07*T* E-l0*T**3

58 52 PRESSURE OF THE REMAINING PRODUCTS f-or BURNUP OF 5X FOR TEMPERATURES LESS THAN <1500 DEG K PHPls-2,782-.l<i7<lE-0«*T+.<138fcE-06*T**2-.^86flE-10*T**3 PMP2*-3.3<l9+.58aaE 03*T+.2792E-06«T** E-10*T**3 PMP3a-3.7<i<H'.5998E-03*T+.32<ISE-0b*T**2-.a07bE-l0*T«*3 PMP<ln-2t 052t-.638f>E-0«*T+.3<J<tfeE-0fe*T**2-.362fcE-10*T**3 PMP5a ,59b3E-03*T+.1171E-0b*T**2»1325E-10*T**3 PMPb*-.I363+.2fe57E-03«T+.53iaE-07*T**2. iai3e-12*t**3 PMP7a.25a7-*'.28b9E-03*T+.2362E-07*T** E-l 1*T**3 PMP8a<l.3aa-.00iab5*T+,2S29E-0b*T»» E-ll»T**3 PMP9«-1.295* «T-.3355E-0feiiiT** E-10*T**3 PMP10=,2833+tl326E 02-*T-.306feE-0fe*T**2+«3241E-10*T**3 FOR TEMPERATURES GREATER THAN 0500 DEG K PMPl= ab57*T-.133aE-05*T** E-09*T**3 PMP2*" *T-.1428E-05*T**2+.la8E-9*T**3 P M P 3 3-5, E i» T -. i a f e 3 E * T i * * E * T * * 3 PMPac-a a3lb*T-,128E-05*T** E-09*T**3 PMP5s 2#8a8+.32blE-02*T-.95aaE-0b*T«*2+.lCa5E-09*T**3 PMPb=-2,bbB *T-,9222E-0b*T*o E-09*T«*3 pmp7s ,002ai5*t-,659be-0b*t** e-10*t**3 PMP8=-l.I93+,0018ia*T-,aa3bE-0b*T** E-10*T**3 PMP9= ,001378*T-.2787E-0b*T** E-10*T**3 PMP10=»aa0a+,00l i 0a*T-.lb58E-0b*T** E-10*T**3

59 PRESSURE OF THE REMAINING PRODUCTS FOR BURNUP OF BX FOR TEMPERATURES LESS THAN 0500 DEG K PMPla-5.lBO *T-.IB69E-05*T**2+.lB22E-09*T**3 PMP2»-3.9BU+,4261E-02*T-.131feE-05*T**2+.lO58E-09*T**3 PMP3*-3.50a+.p3361*T-.113BE-05*T**2+.12O3E-09*T**3 PMPO«-3.2b *T-.1122E-05*T**2*.1218E-09*T**3 PMP5>-2.6BB * T E-0«*T«* E-09*T**3 PMPfe = -2,1 0 2 t,002827*t-,b135e-06*t**2+.6b7e-10*t**3 PHP7»-l,05O *T-.635E-0fc*T** E-10*T**3 PMP8« B81*T-. «B0lE-0fe*T**2+.5O77E-10*T**3 PMP9*-.b8l *T-.3271E-0fe*T**2+.370BE-10*T**3 PMP10»-,a B1228*T-,I9B3E-0fe*T** E-10<rT**3 FOR TEMPERATURES GREATER THAN 0500 DEG K PMPJ * - 0,7 9O +.O573E-03*T+,O972E-0fe*I**2-,613OE-10*T**3 PMP23-O,191 +.B332E-03*T+.36OfeE-0fe*T**2.O(j32E-10*T**3 PMP3 = -2.? E-03*T E-06*T**i E-10*T**3 PMP0* B<JlE-0a*T+.2773E-0fc*7**2-.274BE-10*T**3 PMP5= feE-03*T+.1033E-0fc*T**2-. B795E-11*T**3 PMP6*3.B3B B*T E-0b*T**2-.lB7 7E-10<tT**3 PMP7= *T+.Ub75E-0fe*T**2-.22lE-10*T**3 PMP8=.165lE OE-03*7**l+.lfe06E-06*T**2-.56B8E-ll*T**3 PMP9 =.120lE J513E-0O«7-t-.730BE-07*7**2+.20lBE-12*T**3 PMP10= E-03*1-.303OE-07*T**2+,7379E-11*T**3

60 THE NEXT SET OF ANALYTICAL EXPRESSIONS PREDICT THE PRESSURES OF THE ALKALI METALS. KEY : PAMI PAM3 PAM5 PAMA D T s a a e c PRESSURE OF OF THE-ALKALI METALS FOR BURNUP PRESSURE OF OF THE ALKALI METALS FOR BURNUP PRESSURE OF OF THE ALKALI METALS FOR BURNUP PRESSURE OF OF THE ALKALI METALS FOR BURNUP FUEL SMEAR DENSITY (GM/CM**3) TEMPERATURE (DEGREES KELVIN) a a a C IX 3X 5X 8X PRESSURE OF THE ALKALI METALS FOR Tn0.0 TO T=4000. P AM1'= C2.a« *D+1,299*D**2-. 1B5427*D**3) + T* ( *D *0** 2* *0* *3) PAM3»t-a, A*D-l.637*0**2+.055a9*D**3)* T*C.0B152+, *D *0**2-.00P02178*D**3) PAM5=C2, *D-1.339*D**2+.0B745*D*+3)+ T*C ,003677* *D** *D**3) PAMB=(11,69-11,49*D+,41P9*D**2+»00532*D**3)+ T* C a*D *D** *0**3)

61 55 PRESSURE OF' THE ALKALI METALS FOR T»U000. TO 7^5000 P4Mlc(-8.08ai + l?.231*d-3.163bi*-d** *di**3)f 0015b-,00179bb*D+,000b037*D** *D**3) PAH3=C7. 1 * *D+b.84*D*+2-.2b6a*D+*3)* f*(»,0014b3+.003bb9*d *d**2+.000e583fc>*d**3j PAM5 = C-1/ *D+4,919*D** *0**3)+ T * ( *D *D**2+, *D**3) PAH8=( 4b,85+31,b2*D-.9bb5*D**2-.01b4b*D**3)+ PRESSURE OF THE ALKALI METALS FDR T=5000. TO T= PAM1*( *d-, 89157*D** a57*D**3)* T*(, *D+, *D** E-08*D**3) PAM3=(-4B.42+59,22*D-4.b91*D** *0**3)+ T*(,009bb *D *D** *0**3) PAH5=(-bb *D-8.132*D**2+.3*D**3)* T* C *D *D** *D**3) PAM8= ( *D -l1. 19*0**2+.565*0**3) + T * ( , 01b94*O+,001881*0** *0**3)

62 APPENDIX C U ser's Guide fo r the Improved F issio n Product Pressure Model. 56

63 57 The in fo rm a tio n in th is appendix is broken in to th re e p a rts. In the f i r s t p a rt, the parameters th a t the user must supply are lis t e d according to the card on which they appear. The symbols used are the same th a t are used in the model. Card one re fe rs to the f i r s t card on which the parameters fo r the fis s io n product pressure model appear. The Fortran form at fo r each card is 6E12.5. The second p a rt is a flo w c h a rt (F igure 18)which shows the lo g ic th a t was employed to check the various parameters to see th a t the re te n tio n and tim e delay options had been p ro p e rly a p p lie d. The la s t p a rt is a lis t in g o f the equation o f s ta te subroutine th a t has the fis s io n product pressure model inclu d ed. Some o f the standard o p tions norm ally a v a ila b le in the equation o f s ta te subroutine have been om itted to save space. In a d d itio n to the parameters th a t are placed on cards 1-6, the user must set one fla g to in d ic a te h is in te n tio n to use the fis s io n product pressure model. On the card th a t is numbered card two by the o rig in a l VENUS-II document (ANL-7951 } the user can in d ic a te his d e s ire to include the fis s io n product e ffe c t by p la cin g a 1 in column 26. This sets a fla g so th a t the parameters on cards 1-6 w ill re a d -in and p rin te d -o u t again along w ith the o th e r in p u t d a ta. With the fla g thus s e t, the user may use any standard deck as o u tlin e d in the VENUS-II document sim ply by p la cin g h is s ix data cards on the end o f the data deck. A. The F ission Product Pressure Model Data Deck Card 1 BURN The average burnup o f the core in p e rc e n t. MPRET1 Estim ate o f the minimum fis s io n product re te n tio n fa c to r a t the cente r p o s itio n fo r the rem aining fis s io n products.

64 58 MPRET2 MPRET3 AMRET1 AM RET 2 Estimate o f the fis s io n product re te n tio n fa c to r midway between the center p o s itio n and the core and blanket in te rfa c e f o r the rem aining fis s io n products. Estim ate o f the fis s io n product re te n tio n fa c to r a t the core and blanket in te rfa c e f o r the rem aining fis s io n products. Estim ate o f the minimum a lk a li-m e ta ls re te n tio n fa c to r a t the center p o s itio n f o r the rem aining fis s io n products. Estim ate o f the a lk a li metals re te n tio n fa c to r midway between the cente r p o s itio n and the core blanket in te rfa c e f o r the rem aining fis s io n products. Card 2 AMRET3 NGRET1 NGRET2 NGRET3 TCRTMP TCRTAM Estim ate o f the a lk a li metals re te n tio n fa c to r a t the core and bla n ke t in te rfa c e f o r the rem aining fis s io n products. Estim ate o f the minimum noble gases re te n tio n fa c to r a t the center p o s itio n fo r the remaining fis s io n products. Estim ate o f the noble gases re te n tio n fa c to r midway between the cente r p o s itio n and the core and blanket in te rfa c e fo r the remaining fis s io n products. Estim ate o f the noble gases re te n tio n fa c to r a t the core and b lanket in te rfa c e fo r the rem aining fis s io n products. The delay time fo r the rem aining products from the i n it ia t io n time to the s ta r t o f p re s s u riz a tio n. The delay tim e fo r the a lk a li m etals from the i n it ia t io n tim e to the s ta r t o f p re s s u riz a tio n. Card 3 TRCTG1 TCRTG2 TCRTG3 TMINMP The delay time f o r group 1 o f the noble gases from the in it ia t io n tim e to the s ta r t o f p re s s u riz a tio n. The delay time fo r group 2 o f the noble gases from the i n it ia t io n time to the s ta r t o f p re s s u riz a tio n. The delay time fo r group 3 o f the noble gases from the i n it ia t io n tim e to the s ta r t o f p re s s u riz a tio n. The in it ia t io n tem perature o f the rem aining fis s io n products. This s ta rts the tim e r fo r the rem aining fis s io n products. TMINAM The i n it ia t io n tem perature o f the a lk a li m etals. s ta rts the tim e r fo r the a lk a li m etals. This

65 TMINNG Card 4 The in it ia t io n tem perature o f the noble gases. the tim e r f o r the noble gases. T his s ta rts TMAXMP TMAXAM TMAXNG TAUMP TAUAM TAUG1 The maximum tem perature fo r the ream ining fis s io n products a t which a ll o f the fis s io n products w ill be released i f the user wishes to release the fis s io n product pressures lin e a r ly over a tem perature range. The minimum temperatures a t which the p re s s u riz a tio n s ta rts is TMINMP. I f the user wishes to ignore th is o p tio n, se t TMAXMP=TMINMP. The maximum tem perature f o r the a lk a li metals a t which a ll o f the a lk a li m etals w ill be released i f the user wishes to release the a lk a li metals pressures lin e a r ly over a tem perature range. The minimum temperatures a t which the p re s s u riz a tio n s ta rts is TMINAM. I f the user wishes to ignore th is o p tio n, set TMAXAM=TMINAM. The maximum tem perature fo r the noble gases a t which a ll o f the noble gases w ill be released i f the user wishes to re le a s e the noble gases pressures lin e a r ly o ver a temperatu re range. The minimum tem peratures a t which the p re s s u riz a tio n s ta rts is TMINAM. I f the user wishes to ignore th is o p tio n, se t TMAXAM=TMINAM. The time constant associated w ith the p re s s u riz a tio n o f the rem aining fis s io n p roducts. I f i t is set equal to 0.0 the p re s s u riz a tio n ra te is instantaneous once the delay tim e has been exceeded. The time constant associated w ith the p re s s u riz a tio n o f the a lk a li m etals. I f i t is set equal to 0,0 the p re s s u riz a tio n ra te is instantaneous once the d e la y tim e has been exceeded. The tim e constand associated w ith the p re s s u riz a tio n o f group 1 o f the noble gases. I f i t is set to 0.0 the p re s s u riz a tio n ra te is instantaneous once the delay time has been exceeded. Card 5 TAUG2 TAUG3 The time constant associated w ith the p re s s u riz a tio n o f group 2 o f the noble gases. I f i t is s e t equal to 0.0 the p re s s u riz a tio n ra te in instantaneous once the delay has been exceeded. The time constant associated w ith the p re s s u riz a tio n o f group 3 o f the noble gases. I f i t is s e t equal to 0,0 the p re s s u riz a tio n ra te is instantaneous once the delay has been exceeded.

66 60 NGF1 NGF2 NGF3 NGCPOS The fra c tio n o f the noble gas pressures th a t pressurize according to the parameters o f group 1. The fra c tio n o f the noble gas pressures th a t pre ssurize according to the param eters o f group 2. The fra c tio n o f the noble gas pressures th a t pre ssurize according to the parameters o f group 2. The a x ia l p o s itio n where the minimum noble gas re te n tio n occurs. I t should be expressed in terms o f i t s mesh p o s itio n For example, i f the minimum re te n tio n occured midway between the 14 and 15 mesh c e ll, the cente r p o s itio n would be entered as Card 6 NGCHTH The distance between the cente r p o s itio n and the most d is ta n t c o re /b la n k e t in te rfa c e. This can e a s ily be determined by counting the number o f mesh p o s itio n s from the center p o s itio n to the p o in t where the equation o f s ta te fla g in d ic a te s a change from the core to the b la n ke t. One should count the number o f mesh p o s itio n s in both a x ia l d ire c tio n s and take the la rg e r o f the two d ista n ce s. MPCPOS MPCHTH AMCPOS AMCHTH The a x ia l p o s itio n where the re te n tio n fa c to r o f the remaining products is a minimum. The center p o s itio n fo r the rem aining products. The distance between the center p o s itio n fo r the remaining products and the fu rth e re s t core and blanket in te rfa c e. The a x ia l p o s itio n where the re te n tio n fa c to r o f the a lk a li metals is a minimum. The center p o s itio n fo r the a lk a li m etals. The distance between the center p o s itio n f o r the a lk a li metals and the fu rth e re s t core and b lanket in te rfa c e. B. F is s io n Product Pressure Model Flow C hart The fo llo w in g pages co n ta in a flo w ch a rt to show ju s t how the various re te n tio n and p re s s u riz a tio n fa c to rs were a p plied to the c a l culated fis s io n product pressures. Below are the d e fin itio n s o f the v a ria b le s used in the flo w c h a rt th a t have not p re v io u s ly been defined in the in p u t deck.

67 61 NDT NCYCLE ISP(28) DELT ZPOS T P PMP PAM PNG A fla g th a t is set to make sure th a t delay tim es are a ll incremented w ith each tim e step. The number o f the c u rre n t tim e step o r cycle The fla g th a t is se t in d ic a tin g the users d e sire to include the a ffe c ts o f the fis s io n products. The size o f the c u rre n t time step in seconds. Here the a x ia l mesh c e ll is used to c a lc u a lte an independent v a ria b le th a t in d ic a te s the lo c a tio n o f the c u rre n t mesh c e ll. In the model a ZPOS is c a lc u a lte d fo r each fis s io n product group. The tem perature o f the mesh c e ll. The pressure o f the mesh c e ll. Pressure o f the remaining fis s io n products. Pressure o f the a lk a li m etals. Pressure o f the noble gases. As a m atter o f expediency, F ortran lo g ic n o ta tio n s were used in the flo w c h a rt.

68 Figure 14. (Continued) Flow Chart o f F ission Product Model in the VENUS-11 Disassembly Code. Pressure

69 Figure 14. Flow Chart o f F ission Product Pressure Model in the VENUS-11 Disassembly Code, cn ro

70 64 C. L is tin g o f Equation o f S tate Subroutine On the fo llo w in g pages one can fin d a lis t in g o f the equation o f s ta te subroutine where the fis s io n product pressure model has been inclu d ed. Many o f the standard o p tions a v a ila b le in the o rig in a l VENUS-II equation o f s ta te subroutine have not been in clu d e d. These o p tions included vario u s equations o f s ta te th a t a user could use a t h is o p tio n. Changes in o th e r subroutines and the main program were made to make the new version o f the equation o f s ta te com patible and to a llo w the user to read in the data re q u ire d. These changes included in p u t and o u tp u t form a tin g as w ell as common and dimension statem ents.

71 SUBROUTINE EQUSTA(R,Z,PaTZR,P,THETA,RHOO, KHO, RHONEW, RHONAO, RHONA, EOS 00 1 RHQSSO,RHOSS,RHOUO,RHOU,MASSNA,MASSSS,MA5SU, 2 VFNA,VFSS,VFlj,DELV,H,U,REDV0L,DELC),IMAXP3, 3 JMAXP3,NCYCLE,KT,IUOLD,THETAO,OELT,MASSZR, a AMOT,GNOT,PMl)T) c IMPLICIT REAL»8 (A -H,0-Z ) INTEGER W 1 NGRET3,NGF1,NGF2,NGF3,NGCP0S,NGCHTH,MPCP0S,MPCHTH, 2 AMCPUS,AMrHTH,MVR REAL»8 MASSU,MASSNA,MASSS$,maSSZR COMMON /C/EL,PMl,PHl3,XK,XKLIM,AK,BK,DEL*fl,PZER0,PFINAL,PPSUP, 1 PPAST,EP51,EPS?,EPS3,EPSa,TSTOP, 2 BETA ( 6 ), ALAM(M, C ( 6 ), CO(b),V«HOT ( A ), Ad(5) COMMON /D /T O T V,T M (3 ),F N (3 ),C F (3 ), PFN( 3 ), CF0 ( 3 ), XKOIS( 3 ), XKDOP (3), 1 OUPPr4(20), f.)opp(30),oopla(2p),d0rlb(2?) *DOPI C(20), 2 DOPLN(20), THBARC2 0 ),W T ( 2 0 ), VOL( 2 0 ), X ( 3 ),Y(a) COMMON /t/epm AX,tVKM ln( EVRPAX,EM,fcVC,ERHOST,EALPH,ETSTAR,EPPRIM, 1 EBETAS,EPSrAR,EROKIN,EKDMAX,RHOCRT, E A (2 0 ),E B (2 0 ),E C (2 0 ),E U (2 P ),E E (2 0 ),E F (2 0 ),E G (2 0 ),E H (2 0 ) E IC 2 W ),tj t2 0 ),ta A I2 0 )f EPB(20)»ECC(20)»EGGC20),E H m ( 20)» E l i ( 2 0 ),P R A (2 0 ),P R B (2 0 ),P R C (2 0 ),C P 0 (2 0 ),C P t( 2 0 ),CP2C20) ' CP3120),CP«(2P),CP5(20IfTM fclt(20)»mfuse(20)#epsi1 0(20), > TEMPNA(SP),TEMPSS(20) COMMON /5P1/SP (300.) COMMON /SP 2/IS P (S 0) COMMON /G /NOREG,NH,NZ,NRIN,NZIN,IJK, JJJ,KKK,IFLTMP,IFLPRS,ISTEP2, 1 KTVAPP,IFLC,IFLXKFfIFL3PP,KI1,Kl4,N0ELAY,NTHPPT, NPRSPT, 2 NR5( 2 0 ), NZS( 2 0 ), ITMPPT( 1 0 ), JTMPPT ( 1 0 ), IPRSPT(1 0 ), 3 JPKSPT(IB),11(20),J1(20), 12(20),J2(20), I 3C20),J3(20), l a ( 2 0 ), J a (20) COMMON /H/BURN,AKRET1, AMRFT2, AM RET3, TMINAM,TMINNG, TMINMP, TMAXNG, TMAXMP,TMAXAM,TA0MP,TAUAM,TAUG1,1AUG2,TAUG3,TCRTAM, TCRTMP,ICR TGI, TCRTG2,TCRTG3, NGRET 1,NSRtT2, NGRET3, NGF1,UGF2,NGF3,MPRET1, NGE 1,NGF2,NGF3,MPR'ET1, MPRET2,MPHET3,, MPHET3, NGCPOS, NGCP0S, N NGCMTh, MPCPOS,MPCHTM,AMCPOS,AMCHTM 0IMEN3I0N R CIMAXP3,JMAXP3), Z ( IMAXP3,JMAXP3), PATZR (IMAXP3,JMAXP3),P (1MAXP3,JMAXP3)» theta cimaxps, jmaxp3),rhoo (IIiaxP3, jmaxp3) > RHO (IMAXP3,JMAXP3), KH0NtW(IMAXP5,JMAXP3)» RHONAO(IMAXP3,JMAXP3), RHONA (IMAXP3,JMAXP3), RHOSSOCIMAXP3,JMAXP3),KHOSS (IMAXP3, JMAXP3), EOS 10 EOS 20 EOS 30 EOS ao EOS 50 EOS 60 EOS 70 EOS 80 EOS 90 ECS 100 EOS 110 EOS 120 EOS 130 EOS ia0 EOS 150 EOS 1 bo EOS 170 EOS 150 «E OS 190 EOS 200, EOS 210 EOS 220 EOS 230 EOS 240 EOS 250 EOS 260 EOS 270 EOS 280 EOS 290 EOS 300 EOS 310 EOS 320 EOS 333 EOS 390 EOS 350 EOS 360 EOS 370 EOS 360 EOS 390 EOS 400 EOS ai0 EOS «20

72 6 HHOUO (IMAXP3,JMAXPS),RHOU ( IMA XP3) JMAXPJ}, 7 MASSNA(IMAXP3tJMAXPJ), MA5SSS( IMAXP3, JMAXP3)f 8 MASSU (IMAXP3,JMAXPJ),VFNA (IMA XP3, JMAXP3), 9 VFSS (IMAXP3.JMAXPJ), VFU ( IMA XP3, JMAXP3) DIMENSION OEUV (IMAXPJ,JMAXPJ),h (IMAXP3, JMAXP3), *1.E-6*TEMPSS(K}**3 B1$S *5, BPS S»I,/HlSS PMELT(8)*OexP(-«.34*OLOG(TMELT(K)) /TMEUT(K)*69,979) UMtuT(8 )*(TMtUT(K)»273,0)/ DO 21 IMPX*1, IMAXP3 DO 21 IMPY 1,JMAXP3 GNDT( IMPX, IN PY )*0.0 AMOT(IMPX,IMPY)«0,0 PMOT (IM PX,IM PY)*0.0 NDT *0 EOS 430 EOS 440 EOS 450 EOS 4b0 EOS U (IMAXP3, JMAXPS),HEOVOUUMAXP3» JMAXP3), EOS MASSZR(IMAXP3,JMAXP3)r AMOT ( IMA XP3, JMA XP3), EOS CiN[)T CIMAXP3, JMAXPJ),PMDT CIM A X P 3, J M A X P 3 ) t'o DIMENSION ppp ( 8 2 ) fdelp (8?) EOS 510 DIMENSION KT ( IMAXP3,JMAXP3), IUOLD (IMAXP3, JMAXP3) EOS 520 DIMENSION THETAO(IMAXP3, JM AX P 3), BPINA (20), BBSS (20) EOS 530 DIMENSION PI1EI.T (20) )UMEl TC20) EOS 540 F-OS 550 EGEN *0,5 EOS 580 3P ( 8 ) * 0,0 S P ( 1 I) *0,0 EOS EOS EOS 590 IM A X PI» IMAXP3-2 EOS 800 J M A * P 1 * JMAXP3-2 EOS 610 DO 20 J*?#JMAXM1 EOS 620 DO 20 1 * 2, IMAXP1 EDS 630 P (1,J)*P A T Z R (1,J) EOS 640 DO *lrNOREG EOS 650 IF (N C Y C U.G E.l) DO TO 100 EOS 660 CDMPNAs0,0 CCiMPSS*0.P CllMPF sp, P EOS EOS EOS BtiNA(8)*79, ,045758* I.E-2*TEMPNA(K)+9,707320*l.E-fc* EOS 7 id0 1TFMPNA(K)**2 EOS 710 B1NA*3,59 EOS 720 B 2 N A»1, / b 1 N A EOS (8)* ?*4,295894*1EMPSS(K)-5,530116*i,E-3*TEMPSS(K)**2* EOS 740 EOS 750 EOS 760 EOS 770 EOS 730 EOS 790 EOS 800 EOS 810 EOS 820 EOS 830 EOS 840 EOS 650

73 W W *,50 VV*1.0U B l M P * C M P H E T 2 - M P 9 E T l * C l - R W / V V ) - M P R E T 3 * W W m } / C W W * * 2 - V V * W W ) B2MP* C M P HE!3-M P P E T1»( 1 - V V * * 2 / W W * * 2 ) - M P R E T 2 * V V *» 2 / W w * *? ) / ( V V - V V * * 2 / W W ) eiart*(amret2-amretl*cl-ww/vv)-amret3*ww/vv)/(ww#*2 VV *HW) 02AMsfAHRFT3-AMPfcTl*U-VV**2/WW**2)- AMRE12*VV**?/WW**2)/(VV-VV**2/WW) BlNr.»(NGRET2-NGRETl*U-WW/W)-Nr,RET3*WW/VV)/(WW*A2-VV*WW) B2NGa(N0RETZ NGPETl»(l-VV**2/WH**2)" N G K S T 2 * v y *» 2 /W W * * 2 J /( V V - V V *» 2 / 'W W ) IL*NZS(K) JL*NKS(M 00 90P0 1* 1, a L «J1 C«) J «1,JL M *11 CM- 1 +J X^'JM» COEU3aH(H,L)/RHOOCM,U - PtM,U*DELV(M,L)*l,0E-0T)ARHONEW IF CM (M.U),EQ,3) GO TO 3000 IF CKHOU(M,U»VFU (H,U.E U.0,0 ) GO TO 160 IFCT*lElA(Nf L ],G T t TMELT(K)) GO TO 120 CP* (CP0CM+THETA CM, U * (CPI («) THETA CM, L)*CP2CK)))*RH0U 1*V FU (M,U OELTH«XNUM/CP IFCTHETA (H,t)+DELTH,GT.TMELTCK)) GO TO 110 THE r A ( n, U "THETA (H,U+OELTH UfH.U * 0.0 GO TO 150 XNUHsXNUM-CTHFLT (K)-THETA (M,U) *CP THETA(H,L)*ThF.UTCK) I F ( T HET A(H, L ), GT, T MELT CK) + 10,) GO TO 143 CP«HFUSECM*HHQU (M,L )*V F U (M,1 )*0,1 0ELTH»xnum/CP IF(THETA(M,t)+UEUTH.GT.TMELTCK}+10,J GO TO 130 THETA (M,L)* THETA(M,t)+OELTH U ( m, l 3 * HFUSE (K) * RHOUCM,L) *VFU(M,L) GO TO 150 XNum.X num-cp* CTMELT (K ) 1 0,-THETA(M,L)) THETA(M,U)«TMEUT(K)+10. (M,L) CP* (CP3CK)*THETA(ti,U*(CP4(K)*THETACM,Ll*CP5(K)»*RMQU (M,U.*VFU(M,L) DELTh*XNUM/CP EOS 860 EOS B70 EOS 880 EOS 890 EOS 900 EOS 910 EOS 920 EOS 930 EOS 9a0 EOS 950 EOS 960 EOS 970 EOS 960 EOS 990 E05 ice0 EOS 1010 EOS 1020 EOS 1030 EOS 1040 EOS 1050 EOS 1060 EOS 1070 tns 1060 EOS EOS 1100 EOS 1110 E EOS 1120 EOS 1140 EOS 1150 EOS 1160 EOS 1170 EOS 1180 EOS 1190 EOS 1200 EOS 1210 EOS 1220 EOS 1230 EOS 1243 EOS 1250 EOS 1260 EOS 1270 EOS 1260

74 C C C THETA(M,L)i THETA(M,L)aDELTH ABLE * TmELT(K) +1(5. U(!1,L) «C HFUSt(K) + THETA(M,L) A (CP3(K) THET A (M,L) A l(cpu(k)/2, THETA(M.L) * CPb(K)/3.)) - ABLE * (CP3CK) ABLE * 2?( CP4(K)/2. ABLE * C.P5(K)/3.)1) a RH0U(M,L)aVFU(M,L) EGEN «EGEN+U(M,L)*MASSU(M,L)/(RN0U(M,L)aVFU(M,L5) KTSUB «KT(M,L) GO TO (30 0 0, , , , , , ), KTSUB ANL EQUATION OF STATE 11FFL *0 IP T F L? IAOJ»0 MMM 0 PAVG«P(M,L) POLDaP (M,L) U(I1,L)»KH0NEK(M,L) AU(M,L)/KHO(M,L)+XNUM GO TO 3150 IADJ*1 IF(IU0LD(M,L),E0.1) GO TO 3020 IF('JCB,L)/(RHOU(M,L)*VFU(M,UM000.0>,GE,UMELTCK)) GO TO 3060 C C CALCULATE TEMPERATURES ANO PRESSURES c 3020 IF(TUOLQ(M,L),EQ,2) THETA CM,L3*TMELT(K) + (U(M,L)/ (RHOU(M,L) a 1 VFU(M,Ln-l,E3*UMELT(K))/(HFUSE(K)t0.<l3725«) EEE*U(M,L)/(RHOU(M,L)aVFU(M,L)*1000.) IF (IUOLO(M,U.E0.2) GO TO 3040 T l»s73,+2?87,*tee T?a ( l303.*REDVOL(M,L)+1699.*REDVOL(M,L)aa2) 1*<EE 1 E-(0, »HE0 VOL CM,U)) 1FCT2.LE,16000,0) GO TO 3030 IF (REDVOL(M,l ).L t.h.b) GO TO 3030 T 3«428?,34* (EEE ) T?*()MIN1 (T2, T3) 3030 THETA (ft,l) *0HAx 1 (T 1, T2) 3040 Rl* OEXP(-4.34*DLOG(THtTA(M,L)) /THtTA(M, L)+69,979) IF(IUOLO(M,L).NE.l) EEE«EEb-hFUSE(K)/ PAAsEEE aREDVOL(M,L)a.0767/REDVOL(M,L)*a3 PBB«1.55aE12*0EXP(-9.67aREDV0L(M,L) aREDVOL(M, L ) a * 2) P2.PAA+PB6 IF(REDVOL(M,L),L i,1,) GO TO 3050 EOS 1290 EOS 1300 EOS 1310 EOS 1320 EOS 1330 EOS 1340 EOS 1350 EOS 1360 ECS 1370 EOS 1360 EOS 1390 EOS 1400 EOS 1410 tos 1420 EOS 1430 EOS 1440 EOS 1450 EOS 14 b 0 EOS 1470 EOS 1483 EOS 1440 EOS 1500 EOS 1510 EOS 1520 EOS 1530 EOS 1540 EOS 1553 EOS 1560 EOS 1570 EOS 1580 EOS 1540 EOS 1600 EOS 1610 EOS 1620 EOS 1630 EOS 1640 EOS 1650 EOS 1660 EOS 1670 EOS 1680 EOS 1690 EOS 1700 EOS 1710

75 P C C «l.e 10 /(1.9» P E D V O L (M,U ) EOS 1720 P2«PC C*(EEE *HEDVO L(M,U) EOS P (M,t) «C>MAXi (PI,Pg) E c * * * * * * * * * * * * * * * * * * * - * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * EOS 1750 c ** FISSION PRODUCT PRE55UHE MODEL * * * EOS 1760 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * EOS 1770 I F ( IS P (28).EQ.0.0) GO TO 225 EOS 17e0 DeWHOUCM.L) EOS 1790 T*THETa (H,L) EOS 18U0 PMP*tf,0 EOS 1810 Pam* n. H EOS 1820 PNG*0,0 EOS 1830 IF (NDT.EQ.NCYCm GO TO 230 EOS 1840 DO 1^9 Ii-iPXs 1, IMA*PJ EOS 1850 DO 199 IN P f M, JMAXP3 EOS 1880 A MOT (IMP*,1MPY)*AM!JT CIMPX,I MPT) AOELT EOS 1870 GNOTCIMPX,IMPYJsGNDTCIMPX,IMPYJ+DELT EOS PHOT(1MPX, IMPY)«PMDTCIMPX,IMPYJ+OELT EOS 1690 NOT NCYCLfc EOS ZPOSNGsAHS ( {NGCPOS-L + t,)/(ngcmth)j EOS 1910 ZP05MP3AeS((MPCP0S-L+l,)/ MPCHTH}) EOS 1920 ZPOSAMaAbSt(AMCPOS-Ltl. ) /(AMCHTH)) EOS 1930 IFCZPOSMG.GT.l.) ZPQSNGsJ.O EOS 1940 IFCZPUSMP.GT,1.) ZPOSMP«1,0 EOS 1950 IF CZPOSAM.GT, 1,) ZPOSA(1»l,0 EOS I960 IFIT.GT.TMINMPJGO TO 201 EOS 1970 PMDT(Mf U *0,0 EOS I F ( F,GT, TMIMM) GO TO 233 EOS 1990 AMOT (M,lJ *2.0 EOS IF(T.GT.TMINNG)GO TO 20-5 EOS 2010 GNOT (M,L )*0.0 EOS FGPsPAr.fPNG + PMP EOS 2030 P (M,U *P (M,L )tf G P EOS 2040 GO TO 225 EOS 2050 PRESSURE OF THE M.KACI METALSi IF(AMOT(M,L)-TCHTAM) 253,251,251 EOS IF (T,G T.6 H 0 l,a N O.P.L T,4,) 0 *4,0 ECS 2080 IF ( t URN, L T,3,) GO TO 410 EOS 2090 IF CBURN.LT,5.) GO TO 423 EOS 2100 IFCBUHN.LT,8.) GO TO 433 EOS 2110 GO TO 440 EOS 2120 c *** PRESSURE OF ALKALI METALS FOR 0UHN*1 EOS IF (T,G T,S ) GO TO 415 EOS 2140

76 IF(T.G T.4001,) GO TO 414 EOS P A K i«(2, * *1 )**? *0 **3 ) + EOS 2160 X T * ( -, 0011, *0 -, * 0 * * 2 *. 00O08108*0* *3) EOS 2170 GO TO 4 Ib EOS PAM1 ( - 8, J + l?,? 3 t* * 0 **2 +, * 0 **3 )+ EOS 2190 X T * ( b -, *0+.0CH)603 7 *0 ** *0 **3 ) EOS 2200 GO TO 416 EOS PA M 1«( , * *0 ** *0 **3 )+ EOS 2220 X T * l P31915*D +.O *0 ** E-08*D **3) EOS IF ( HuWN. GT, 1, ) GO TO 420 EOS 2240 P ' M r r A111 EOS 2250 GO To 400 EOS 2260 c *** PRESSURE Op' ALKALI METALS FUR thjrn*3 EOS IF ( T,GT, ,) GO TO 425 EOS 2280 IF (T,G T.4001.) GO TO 42f ECS 2290 PAM3 = ( * *0** *0 ** 3) + EOS 2300 X T *( O P 6574*U +, *0 **2 -, *0 **3 ) EOS 2310 GO TO 426 EOS PA*i33(7,145-8,4 65* * 0 * * 2 -, *0 **3 ) + EOS 2330 X T *(-,0 O , *0 -,( *0 **2 +, *0 **3 ) EOS 2340 GO TO 426 EOS PAM3«(-4B, ,2 2 *0-4,6 9 1 * 0 * *2 +, * 0 ** 3 )+ EOS 2360 X T «(,0( ( *D+, *0 **2 -, *0**3) EOS IF(BUMN.l'T,3.) GO TO 430 EOS 2330 PArt*PAM3-((PAM3-PAM1)*((3.0-8 U R N )/2.)) EOS 2390 GO TO 400 ECS 2400 c**» PRtSSUHF OF ALKALI METALS FOR BURN=5 EOS IF (T.G T.5O 01.) GO TO 435 EOS 2420 IF (T.G T.4001.) GO TO 434 EOS 2430 PAM5»( 2, «D * 0 ** *0 **3 )+ EOS X T* ( *0 +.00U * 0 ** *0 **3 ) EOS 2450 GO TO 436 EOS PAM 5«(-1 4, * *0 * *2 -, * 0 * *3 )+ EOS 2470 X T* ( , * *0 **2+, *0**3 ) EOS GO TO 436 EOS PA(15* (-6 6, ,2 4 * 0-8, 1 3? *0 **? +,3 *D **3 )+ EOS 2500 X T * ( *0 +, *0 **2 -, *0 **3 ) ECS IF (BUKN.GT.S.) GO TO 440 EOS 2520 PAM«PAM5-((PAMS-PAM3)*((5. -BURN)/2. )) EOS 2530 GO TO 400 EOS 2540 c*»* PRESSURE OF THE ALKALI METALS FOR BURN»8 EOS IF (T,G T ) GO TO 445 EOS 2563 IF CT.GT.4001 ) GO TO 444 EOS 2570

77 PAM8* ( ,4 9 *0 +,4 l8 9 *0 **2 +,B *0 **3 )+ EOS 2500 X T* ( , *D -, *0 ** *D**3) EOS 2590 GO TO 446 EOS PA M 8*(-46, ,6 2 * 0 -, * 0 * * *D**3)+ EOS 2610 X T* ( *D -, *0**2+, *0**3) EOS 2620 GO TO 446 EOS PAMHb (-5 1, * * 0 * * 2 +,5 6 5 * 0 * * 3 ) + EOS 2640 X T* ( , *0 +, * 0 * * 2 -, *D**3) EOS IF(BUrtN,GT,B.) P U R N» 8, EOS 2660 PAM«PAM6- ( (PAM8-PAM5)* ( 18,0-BUNN)/3,3 ) EOS IF (P A H,L I,2) PAMip.0 EOS 2680 PAMbPAM* (01AM«ZP05AM**2 + B24M*ZPOSAM + AMBETI) EOS 2690 IF(TMAX*M,tO,TMINAi+)GO TO 405 EOS 2700 YTTTY* (T-TMINAM)/ (TMAXAH-TMIN4M) EOS 2 M 0 PAM*PAM*(0MIN1 (1,L'U,YYYYY3) EOS IFCTAUAM,GT,0,0.ANO. (TCRTAM-APOT ( M,U ), IE. 0,0) EOS X PAM*PAM*(1,-OEXPCCTCRTAM-AMDT CM, L3 ) /TAUAM)) EOS 2740 PAMbPAM*!,0) EOS GO TO 204 EOS PAM*0,U EOS GO TO 204 EOS 2780 PRESSURE OF THE NOBLE CASES IF ( C»m!JT (M»L)-TCRTG3) 256,255,255 EOS IF (GNOT(M,l)-TCHTG2) 257,255,25 5 EOS IF (GNDT (M,L)-TCRTG1) 254,255,255 EOS HEOVt)U(M,L] «RHOCHT/RHOU(M,U EOS 2830 MVRB0.6 EOS 2840 V R 0 * 0,6 EOS 2850 FACbO.5 EOS 2860 U U * (T /2287, EOS 2870 IF (T, L t. TMELT (K )) UU«UU-HFUSE(K)/ ,0 EOS 2880 PP1»DEXPC69,97 9D ,D0/T-4,34D0*OL.OG(T3) EOS PF2»l,554fci2*(UU -3,59+0,119*M VH+0,0767/M VR**3)*EXP(-9,67*HVR+ EOS 2900 X 4,445*MVR*«2) EOS 2910 IF (PP1.GE.PP2) GO TO 222 EOS 2920 FAC«FAC/2,0 EOS 2930 IF (FAC.Ufc,1.E-0B) GO TO 223 EOS MVVRO* ( 1,-FAC) EOS 2950 GO TU 220 EOS VRO»MVH EOS 2970 IFC0A3SCPPI-PP2J.G T.0,0 1 *P P l) GO TO 221 EOS PNG» 21S1,*BURN*T/(REDV0L(M,U-VR0) EOS 2990 PNG*PNG*(B1NG*ZP0SNG**2+B2NG*ZP0SNG+NGRET1) EOS 3000

78 P C A T 1 * N G F 1 * P N G EOS P C A T 2 * N G F?» P N G EOS PC A T3 *N G F 3 * P N G EOS IF CT AUG 1.GT.0.13.ANO. CTCRTC-1- G N U T ( M, L ) ). L F ) EOS X P C A T l» P C A T l * C t - D X P t ( T C R T G 1 - G N D T ( M, U ) ) / T * U G 1 ) ) EOS IF ( T A U D I. G T. 0, 0. A N D. (T C R T G 1- G N O T C M,U ). G E, 0, e) P C A T 1 *0,0 EOS IF C C T C R T G l - A M D T f M, U ). G E. 0, 0 ) P C A T 1* 0.0 EOS l F ( T A U G 2. G T A N O. C T C R T G 2 - G N O T ( M fl ) ). L E ) EOS X P C A T 2 = P C A T 2 * ( l - D E X P C ( T C K T G 2 - G N U T ( M, L ) J. / T A U G 2 ) ) EOS 3090 I F ( ( T C R T G 2 - A H D T ( M, D ).GE.P.fl) PC AT a» 0.0 EOS 3100 c EOS c EOS c EOS c EOS 3140 c EOS c EOS IF ( T A U G 2.GT.0,0, ANQ, ( T C R l G 2-r,Nt)T(M,L)). G E. O. 0 ) P C A T 2 * 0. 0 EOS I F( T AUG3.GT,0.0.A N D, ( T C R T G 3 - G N O T, IE. 0.0) tos X PCATi*PCAT!3* ( 1 - D E X P C ( TC RT G 3 - G N D T CM, L)) / T A UG 3 )) EOS I F C C T C R T G 3 - A M D T C M, U }, G h. 0, 0 ) P C A T 3 «0. 0 EOS I F C T A I I G 3. G T. P. 0. A N D. ( T C M T G 3 - G N O T C M, L) ), GE. 0.0) P C A T 3 * 0, 0 EOS 3210 P N G = P C A T 1 + P C A T 2 + P C A T 3 EOS I F ( T M A X N G. E Q, T M l N N G ) G O T O EOS w WW U N = ( T- T H I N N G ) / C T MA X N G - T M I N N O ) EOS P N G * P N G A C D M I H I C l. 0 0 # W W H W W ) ) EOS G O TO 206 EOS # P N G * 0,0 EOS 3270 GO TO 206 EOS c * * * * * * * * * * P R E S S U R E OF THE R E M A I N I N G F I S S I O N P R O D U C T S * * * * * * * * * * * * * EOS IF (PHOT CM,U-TCRTMP> 25 >#25 3, EOS IF C O. G E ) 0 * EOS F ( 0, C.T. 1, 1 0 * 1. 0 EOS 3320 IF C H U R N. U T, 3.) GO TO 518 EOS IF C d u R N. L T, 5. ) GO TO 610 EOS IF ( J U M M. L T. B. ) GO TO 710 EOS GO TO 210 EOS c * * * P R E S S U R E OF M I S C F I S S O N P R O D U C T S FOR B U R N * 1 EOS I F ( O. L T. 3. A N U. T. L T ) G O TO 593 EOS I F C T. G T , AN D, D,LT,fl,99) GO TO EOS R«1, 15 EOS DF *0- (h a 1,0) EOS IF C D F, G E, 1,0) GO TO 550 EOS IF (T.LT, # ) GO TO 551 EOS

79 GO TO (5 6 1,5 6 2,5 6 3,5 6 4,5 5 5,5 6 6,5 6 7,5 6 8,5 6 9 ),W EOS GO TO (5 7 1,5 7 2,5 7 3,5 7 0,5 7 5,5 7 6,5 7 7,5 7 8,5 7 9 ),W EOS CONTINUE EOS Jfl PMJ>l>3,803-,C!03R8?*T E -e 5 * T * *2 -. IV5 33E -09*T**3 tos 3470 PM Pg ei *t E-(?8*T**2-,O O 48E-10*T **3 EOS 3480 PMPll«(pMPg-PMPi)*0F+PMPl EOS 3090 GO TU 5110 EOS PM P?*1.522-,0017 7*T b'-i16*T**3-.oa43E-10*T**3 EOS 3510 P P P 3 2-1,3 5 8 *, E -0 3 *T «E -0 6 *T **2 * a E -lp «T **3 EOS 3520 PMPJ 1 * (PMP5-PMP2) *UF+PMP2 EOS 3530 GO TO 500 EOS PM P5«-l ,99? 6E -03*T -,248O E -06*T **2+.366rtE -10*T **3 EOS 3550 PMPil s-g, 025+, P01 685* T * T**2+, * T**3 EOS 3560 PMP11*(PMP4-FMP3)*UF*PMP3 EOS 3570 GO TO 500 FOS P M P 4»-2,O *T «3 E -0 6 *T ** O E -in *T **3 EDS 3590 POP 5 * B?+,?367E-02 + T E -06*T**2 +, E -1 0 *T **3 EOS 3600 PMP 1 J a (PMP5-PMP4) *l)f + PNPO ECS 3610 GO LOS 36g0 575 P M P 5 * t, E -0 2 *T -, E -0 6 *T ** E -1 0 *T **3 EOS 3630 P M P h x E -0 2 *T -, E -06 *T **2 + t t"1 0 *T **3 EOS 3640 PMP 11» (prip6-pmp5)» 08 P M P 5 EOS 3650 GO TO 5P0 EOS 36b0 576 PMf,6 * -2,9 b 9 *, F -0 2 *T E -0 6 * T * « t-1 0 *T ** 3 EOS P M P 7 *-g ? *T E -0 6 *T «*2 * E -lo *T **3 EOS 3680 PMP 11 * (PMP/-PMP6) *0p + PMF 6 EOS 3690 GO TU 500 EOS P P P 7 *-2,6 fl6 *, *T -, E -O 6 *T **2 t E -t0 4 T **3 EOS P H P 8.X -1,99*,002014*T -,5P 2«E -05*T **2+,5812E -10*T **3 tos 3723 PHP11*(PMP6-PMP7)*0F+PMP7 EOS 3730 GO TO 500 EOS PMP8 = ,0 32 (U 4 i» T -.5 P *T ** E-17,*T **3 EOS 3750 P N P 9 = -l, b *T P E -0 6 *T ** B 9 E -1 0 *T **3 EOS 3760 PPPiI *(PMP9-PMP6)xOF+PMPH EOS 3770 GO TO 500 EOS P M P 9 *-1, ,0 0 J *T -, E -0 6 *T *«2^.4 0 B *T **3 EOS 3790 P H P IB i-l.5 9 g», g 6 *T g E -0 6» T **2 ^, E -1 0 *T **3 EOS 3800 PMPJ1» (PHP10-P0P9)*DF+PFP9 EOS 3810 GO TO 503 EOS P M P t* -l,5 2 6 * E -0 3 * T +,lg 8 8 E -0 6 * T * * 2 *,1189E-10*T**3 EOS 3830 PMPg« , 1714E-03*T +,? E -0 6 *T **2 -, E -1 0 *T **3 EOS 3840 P0P11«(PmP 2-p m p i)» of+pmp1 EOS 3853 GO TO 530 EOS 3860

80 562 P M P 2 t-?,p 95+,1714E -03+ T +.2«73E -06*T ** E -10+ T **3 EOS 3970 P M P 3 = -2,2 3 t E -0 3 *T E -3 6 *T ** E T **3 EOS 3880 PrtP 11 * (PMP3-PMP2) *()F + PHP2 EOS 3890 GO TO 500 EOS PMP3» - 2, E T +,4203 E -0 6 *T **2 -, fc>10 + T**3 EOS 3910 P M P 4 *-3, , E -0 3 *T +, t-0 6 *T **2 -,4 0 5 E -t0 + T *» 3 EOS 3920 PMP1 1 * (PMP4-PMP3)*0F+PmP3 EOS 3930 GO TO 500 tus P M P 4t-3,581+,4351E-03* T *, E -0 6 *T **2 -,4 0 5 E -1 0 *T *«3 EOS 3950 P M P 5» , E -0 3 *T +, E -0 6 *T **2 -,4 3 9 ie -1 0 *T **3 EOS 3980 P h P l1s IPPP3-PHPU)*0FtPMP4 EOS 3973 GO TO 503 EOS P H P 5 «-5, ,1432E-33+T+, 3957E -06*T * * E - 10 *T **3 EOS 3993 PM P6.-1, b46E-04»T k )6 *T **2 -t 31«4E-t0i*T**3 EDS 4030 PPP1 1* (PMP6-PMP5)*DFtPMP5 EOS 4010 GO TO 5K0 EOS P M P M -i, E -04*T*,3 1 5 E -0 6 * T * *2 -.3 t4 4 E -1 0 * T * *3 EOS 4033 P M P 7» E T +,t4 7 6 E T **2 -,1180E-10*T**3 EOS 4040 PMP1 1 c (PMP7-PPP6)+0F+PPP6 EOS GO TO 530 EOS PrlP 7 * - 1,0 5 6 *,2405E-03*T+, E -0 6 * T * * 2 -,1180E-10*T«*3 EOS 4073 P K. P 8» ,!9l9E -04*T +.4B 22-07«T + *2 +, E -tl*t +»3 EOS POP 11 * (PMP8-HMP7)*DF+PMP" EOS 4390 GO TO 500 EOS P P P 6 «l.p m -0 4 *T +.4 0? 2 E -0 7 * T * *2 +, E «l1 * T «* 3 EOS PM P9» P 8b*T-.2521E -06»T*+2+,1584E -10*T**3 EOS PHPU» (PMP9-PMPSO *0F+PI1P8 EOS 4130 GO TO 500. tos P M P 9a-i,29B +,002O B 6*T -,? 521E -06*T ** E -10*T **3 EOS 4153 P M P 1 0 *,6 b E -0 3 *T E -0 7 *T «*2 +,i *T **3 EOS PMP1 1» (PMP10-PMP9)*DF+PMP9 EOS GO EOS PMP11*0. 60S 4190 GO TO 500 EOS P0P1 1 * (2,7 8 -, *D *D ** E -0 1 *O **3 )+ (T *C,1057E-G3 EOS 4210 X *D *O *+ 2 +, E -0 5 *Q **3 )) EOS ae JF(BUHN.GT.l) GO TO 610 EOS 4230 PMPaPPPl 1 EOS 4240 GO TO 300 EOS 4250 c**» PRESSURE OF MISC F1SSIGN PROOUCTS FOR BURN«3 EOS IF IT.G T,b t ANO,D,UT,5.5) GO TO 695 EOS W» l,15 EOS 4260 DF*O (W*1,0) EOS 4290

81 IF (O F,G E.1,0 ) GO TO 650 EOS 4300 IF (T,L T,4500,) GO EOS (1310 GO TO (6 6 1,6 6 2,6 6 3,6 6 4,6 6 5,6 6 6,6 6 7.,6 6 8,6 6 9 ),W EOS GO TO (6 7 1,6 7 2,6 7 3,6 7 4,6 7 5,6 7 6,6 7 7,6 7 8,6 7 9 ),W EOS CONTINUE EOS P M P l*-2.47b-.'l92a E-04*T +.396E-06*T E -1 0 *T **3 EOS 4350 PMP2» , 31 49E-03+T+, 3611 E-06* T* + 2 -,4 2 1 E - 10 *T** 3 EOS 4360 PMPj}a(PMP2-pMPi)*0F+PHPl EOS GO TO 600 EOS PM P2*-3,30S+,314 9E-03*T +.3 M le * T * * 2 -,4 2 le * T * * 3 EOS 4390 PMP3s PiE-i7l4 + T +.< l7 3 0 E -3 6 *T **2 -.5 l3 9 E -l0 *T **3 EOS 4400 PMP33s(PHPJ-PMP?)*0F+PpP2 EOS OK 10 GO TO 600 EOS P M P 3 * -2, ,9 5 e ie -0 4 *T E -0 6 *T **2 -, E -1 0 *T **3 EOS 4430 PMP<1i -2,(! E-04*T+.4223E-06*T**2-,4498E-10*T**3 EOS <1(1(10 PMP33* (PMP4-PHP3) *0F + PflP3 EOS 4450 GO TO 633 EOS P M P 4*-2, ,S 49 9 E -0 4 *T +.4? 2 3 E -0 6*T **2 -,fl4 9 8 E -1 0 *T **3 EOS PMP5* - 2, , E-03*T+. 24 I6 C -0 6 *T * * 2 -, 261BE-10*T** 3 60S 4460 PMP33*(PMP5-PMP4)*0F+PPP4 EOS 4490 GO TO 600 EOS P1P5s E -0 j*t +.? O 1 6 E -0 6 *T **2 -t 2618E-10*T**3 EOS 4510 PM P6*-, E-03*T E -0 6 * T * *2 -,8841 E - l l * T * * 3 EOS 4520 PPP333(PMP6-PMP5)*0F*PMP5 E GO TO 600 EOS PMP8*-, F T + #l3 5 4 E * T * * a ie - ll* T * * 3 EOS 4550 PMP7s ,1199E -03+T +, E -06 *T ** E-10*T**3 EOS 4560 PMP33a(PMP7-PMP6)*0F+PMP6 EDS 4570 GO TO 603 EOS P M P 7 * E -0 3 *T E -0 6 *T **2 -f 1052E-10*T**3 EOS 4590 P M H 8*, E -0 3 *T E -0 7*T **2 -, E -1 2 *T **3 EOS 4600 PMP33*(PMP6-Pf1P7)*DF+PMP7 EOS 4610 GO TO 600 EOS P M P B * , E -0 3 *T E -0 7 *T **2 -, E -t2 *T **3 EOS 4630 PHP9*.359«+,28eE -03*T+,6 733E-07*T**2 +, E -1 2 *T **3 EOS 4640 PMP3 3 * (PMP9-PMP8J+0F+PMP8 EOS 4650 GO TO 600 EOS PM P9*, E -03*T+t E -0 7 *T ** E -1 2 *T **3 EOS 4670 PMP 10«.2337, F.-0 3 *T E -07 *T **2 -, 2416E-11*T* *3 EOS 4680 PMP33*(PMP10-PMP9)*DF+PMP9 EOS 4690 GO TO 603 EOS P M P l« , *T E -0 6 *T ** E -10 «T **3 EOS 4710 PMP2*-3, , * T -, 6 051E -06*T»*2+,8988E -10*T *«3 EOS 4720

82 PMP33»IPMP2-PMP1)*DF*PMP1 EOS TO 600 EOS P M P 2» ,002878*T -,8e51E -06+T *+2+.89B 8E -10*T **3 EOS 4750 P M P 3 «-2, , F T E -0 6 *T **2 +, *T **3 EOS 4760 PMP 53*(PMP3-PMP2)+0F+PMP2 EOS 4770 GO TO 6K0 EOS P M P 3 * E -0 2 *T E -0 6 *T * E -lfl*t **3 EOS 4790 PM Pa* E-02*T-.i5'i83E-05*T»*2t, *T*<*3 EOS 4800 PMP338(PMP«-PMP3)».QF + PMP3 EOS 4810 GO TO 600 EOS «PM F4s-3, eE -02*T-,1083E-ei5+T**2+,1186E-09*T*+3 EOS 4830 P!'iP5*-2.360P.?73?E 8 2 *T -.8? *T **2 +, E -1 0 *T *«3 EOS 4840 PHP33«(POP5-PMPa) +UF+PMP4 ECS 4850 GO TO 600 EOS P M P 5* ,2732E -O 2*T -,8? 3,?E-06*T+*2+,9a85E -10*T**3 EOS PM P6.-?.4P5+.?777E 0? *r-.7994e -0h *T +»2+.88B 5E -10«T **3 EOS 4880 PMP33= IPHP6-PMP5)*06 P MP5 EOS GO TO 6?0 EOS 49E0 676 PM P6»-2,4P5+t E -0 2 *T -, E -0 6 «T» *2+,B E -l0 *T **3 EOS 4910 P H P 7«-t,7 76 +,2 1 7 S F -0? *T -, E -0 6 *T b 5 32 E -1 0 *T **3 EOS 4920 PMPJ3»(PHP7-PMP6)+0F+PMP6 EOS 4950 GO TO 600 EOS P M P 7 * ,2 l7 5 E -0 2 *T E -0 6 *T» *2 *, ie *T **3 EOS 4950 P M P 8 i-l,1 8 +, *T E -0 6 *T **2 +,4 5 1 E -1 0 *T + *3 EOS 496e PPP35 = (PMP8-PMP7) + 0F + PMP"/ EOS 4970 GO TO 600 EOS P M P 8 «-l,ib +,0 0 l6 2 1 *T -,3 8 4 te -0 6 *T **2 +,a 5 1 E -1 0 *T **3 EOS 4990 PM P 9« E -02 *T E -0 b *T **2+, E T **3 EOS 5000 P MP 33 * (PMP9-PMP8)+0F + PMP8 EOS 5010 GO TO 600 EOS PMP9i -, ,1 101 F.-02*T E -06*T **2*,27 37E -10*T**3 EOS 5030 P M P 1 0 s E -0 3 *T «8 E -0 7 *T **2 +,ia 5 1 E -1 0 *T **3 EOS 5040 PMPJ3=1PMP10-PMP9)*OP+PMP9 EOS 5050 GO TO 600 ECS PMP33«U,64 7+,081P2 + O -,0;>665*O ** * 0 * * 3 ) CT*C.5768E-04 + EOS 5070 X,51 18E-P E-04*O*>* E-05*O**35 } EOS IF (PURN.GT,3) GO TO 710 EOS 5090 PM P*PM P33-((PM P33-PM Pll)*((3.-b U R N >/2.)) EOS 5)00 GO TO 380 EOS 5110 C *»* PRESSURE OF MISC FISSION PROOUCTS FOR BURNiS EOS IF (T,GT, ,AND,D,IT,5,5 ) GO TO 795 EOS R» 1 #15 EOS 5140 O F«D-(W *l,0) EOS 5150

83 1F(DF.GE,1,0) GO TO 750 EOS 5160 IF(T.IT.#500,} GO TO 751 EOS 5170 GO TO (761,762,763,76a,765,766,767,768,769),«EOS GO TO (771,772,773,77fl,775,776,777,778,779),W EOS CONTINUE EOS FMPl«-?.782-.ia7aE-0a*T+.a386E-06*T<»*2-,«898E-10»T**3 EOS 5210 PPP2«-3.349*.50a<(E-03*T+,2792E-06*T**2-,3S39-10*T**3 EOS 5220 PMP55* (PMP2-PMP1) *L)F + PMPl EOS 5230 GO TO 700 EOS PMP2* O4F-n3*T+.2792E-06*T** E-10«T**3 EOS 5250 PMH3s-S. 74u+.5995E-03*T +,3246E-C)6*T*»2-.a076E-10*T»*3 EOS 5260 PMP55*(PMPJ-PMP2)*PF+PMP2 EOS 5270 GO TO 700 EPS PHP3*-3,7aa+,5998E-03*T+.32«6E-06*T**2-,a076E-10*T**3 EOS 5290 PMpaB-2,052+,6388E-0a*T+.3«<l6E-06*T**2-,3b26E-10*T**3 EOS 5300 PMP55»(PMPU-PMP3)0DF+PMP3 EOS GO TO 700 EOS «PMP««-2,PI a*T +,3M6fc-06*T**2",3626E-10*T**3 EOS 5333 PMP5*-l,839t.5963E-03*T+.1171E-06*T*»2-,1325E-10*T**3 EOS 5340 pmp5be(pmpg-pmpa)«of+pppa EOS 5350 GO TO 700 EOS PMP5«-1.939t.5963E-P3*T+.117lE-06*T**2-.13?5E-10*T**3 EOS 5370 PMP6i-,1383+,?657E-03*T+t531<lE-07*T**2-,l«l3-12*T*93 EOS 5380 PMP 55 * (PMP8-PMP5) *L)F + PMF5 EOS 5390 GO TO 700 EOS PMP6« E-W3*r*,531«E-07*T**2-,iai3E-12*T**3 EOS PMP7«, E-03*T+,2362E-07*T** E-il*T**3 EOS 5420 PMP55»(PFP7-PPP6)*0FtPPP6 EOS 5430 GO TO 75? EOS PMP7».2547+,2869E-03*T+.2362E-07*T** E-11»T**3 EOS 5450 PMP8»a.3aa-.001O65*T+,2629t-0b*T**2-,52e5E-l1*T**3 EOS 5460 PMP55«(PMPB P«P7)*UF+PMP7 EOS 5470 GO TO 700 EOS PMPe*a.$aa-.00i«65*T+,2629E-06*T**a-#5285E-ll*T**3 EOS 5490 PPP9c ,0018B8*T«.3355E-06*T**2t,3031E-10*T**3 EOS 5500 PMP55*(PMP9 PPPP) 6DF + PPP8 EOS 5510 GO TO 700 EOS PMP9»-t,29g *T-.3355E-06*T*62+,3031E-10*T<i*3 EOS 5530 PMP10« ?6E-02*T-.3066E-06*T** E«10*T»*3 EOS 5540 PMpgg. (PMP10-PMP9)*DF*PMP9 EOS 5550 GO TO 700 EOS 55E PMPl»-5,070+,00fi657*T-,1334E-05*T**2+,1397E 09»T**3 EOS 5570 PMP2»-5,352+,005*T-, 1428E-B5*T**26,148E-9*T**3 EOS 5580

84 PMP55* (PMP2-PMP1) *ijr + PMPi EOS 5590 GO TO 703 EOS PM P5«-5.35P^.005*T-.1«28E-05*T**2+.-1<»8E-9*T**3 EOS 5610 PMP!5*-5.139*. 501 IE -32* T E -05*T * *? *. 1537E -09*T**3 EOS 5620 PMP55s(PMP3-PMP?)*DF+PMP2 EOS 5630 GO TO 703 EOS PMPje-5, IE -0 2 * T -, lflb 3 F -0 5 *T **2*. 1537E»09*T**3 EOS 5650 PMP9s-o.p<?3 +,009 3.i6 *T E -0 5 *T «*2 *,l3 7 3 E -0 9 *T **3 EOS 5660 PMP55*tPMP«-PMP3)*OF+PMP3 EOS GO TO-700 EOS «PMP««-9,093«' *T -, l? 8 E -0 5 «T **2 +, E -0 9 *T **3 EOS 5690 P O P 5» ,3 2 6 le -P 2 *T -,9 5 4? E -0 6» T **2 +, E -0 9 *T **3 EOS 5700 PMP5Sc CPflP5-PPPa) *OF + PMPO EOS 5710 GO TO 730 EOS P H P 5» -2.8 «0 +,3 261E -0? *T -.954eE «06*T ** E -09*T *»3 EOS P M P 6 t «* ie 7 *T -.9 2? 2 E -P 6 *T **2 +, E -0 9 *T **3 EOS P M P 55 =>(PMP6 PMP5)*UF+PmP5 EOS 5750 GO TO 700 EOS b P M P 6 = ia 7 *T -.9?? 2 E -0 6 *T **2 +, E -0 9 *T **3 EOS PMP7s-1.828t-.Pfl2<il5*T-,6596E-06»T**2 +, E -l0 *T *«3 EOS 5780 PMP55»(PMP7-PMP8)*DFtPMF8 EOS 5793 GO TO 7?0 EOS P tfp 7» O 0? 91 5 *T E -0 6 *T ** E -t0 *T **3 EOS 5810 PMP8» a *T -,M 3 6 E -0 6 * T * * 2 *.5 0 S 8 E -1 0 * T * * 3 EOS 5820 PHP 55 * (PMP8-P0P7) *0F+PPP7 EOS 5830 GO TO 700 EOS P n P «* *,P «l-t E -0 6 *T **2 * *T»» 3 EOS 5850 P M P9*-, * * E -0 6 *T **? * E -1 0 *T **3 EOS 5860 php55a(phpq-pmpe)*0ftp«f8 EOS 5870 GO TO 700 EOS P M P 9 *-, * *T -,? E -0 6 *T ** *T **3 EOS 5890 POPl0«-.q«;ia +,M 0ll0 a *T a E -0 8 *T *o a E -t0 *T < r*3 EOS 5930 P M P 55»(PMP10-POP9)*0F+PMP9 EOS 5910 GO EOS PMP5S*!?, » D +, *D * * *D * *3 )*(T *(-, EOS 5933 X +.tp0<jf * E-0 4*D ** E-05 * 0 * * 3 ) ) EOS IF (BURN.UT.5.) GO TO 810 EOS 5950 PMPtpMP55-((PMP55-PMP33)* CC 5.-8U R N )/2,)) EOS 5960 GO TO 300 EOS 5970 C** PRESSURE OF RISC FISSION PRODUCTS FOR 8URN*8 EOS J0 IF IT, GT,6000, AND, D,LT,5.9 )' GO TO 695 EOS W *l, 15 EOS 6000 DF»O-(W*1,0) EOS 6010

85 IFC O F.G E.l,0) GO TO 850 EOS 6020 IF ( T,IT.4 5 P 0,) GO TO 851 EOS 6030 GO TO (8 6 1,8 6 2,8 6 3,# 6 4,8 6 5,8 6 6,8 6 7,8 6 8,8 6 9 ),W EOS 6040 #51 GO TO (8 7 1,8 7 2,8 7 3,B 7«,8 7 5,8 7 6,8 7 7,87B,8 7 9 ), W EOS CONTINUE EOS P'lPl * - 5, 184 +, (105363* T -. J 669E-05* T m E -0 9 *T **3 EOS 6070 PMP2S ,a E -0 2 *T -, E -0 5 *T ** E -0 9 *T **3 EOS 6080 P M P 88 = (Pf1P2 Piv'P l) +DF+PMP1 EOS 6090 GO TO 800 EOS 6100 era P'lP2« le -0 2 * T -. t316fc'-05*t*« *T * *3 EOS 6110 PMP3«-3,504 +,r P3Ol * T E-05 + T , 12«3E-09*T**3 EOS 6120 PWP88*(PMP3-PMP?)+DF+PMP2 EOS 6130 GO TO 8PC EOS PM P3* , T E-eS*T** E-09*T**3 EOS 6150 PMPO« ,0O *T -. 11P2E-05*T** E -0 9 *T **3 EOS 6160 PMPflfl * (PMP4-PMP3) * 0 P + P M P 3 EOS 6170 GO TO 600 EOS PMP<te-J.267+,003759»T-t E -0 5 *T **2 +,1 2l8 E -0 9 *T *» 3 EOS 6190 PHPb» * IE -0 6 *T * * 2 +, E -0 9 *T **3 EOS 6200 PMP8 8* (PHP5-PMP6) +0F+PPP4 EOS 6210 GO TO 800 EOS PM PS*-2.6 * 8 +, * T -,9911E -B 6 *T **2 +,1 C 8 3 E -0 9 *T **3 EOS 6230 P M P M -2.1C 2+,0O? 827*T -,P 135E -06*T *82+,887E -10*T + *3 EOS 6240 PMP68=(PMP6-PTP5)»08+PNP5 EOS 6253 GO TO 800 EOS p P P 8» -2, , T - t E -0 6 *T **2 +,8 8 7 E -l0 + T **3 EOS 6270 P M P 7 * O 1 *T -,6 3 5 E -3 6*T **2 +, E -1 0 *T **3 EOS 6280 PMP88* (PMPf-PMPfc)+0F + PMP6 EOS 6290 GO TO 803 EOS P P P 7*-1,U 5 U +,00? 2 8 1*T E -C 6*T **2 +, E -1 0 *T **3 EOS 6310 PMP8«-1, * T -.a E -0 6 *T ** E -l0 *T **3 EOS 6320 PPP68S(PMP0-PMP7)*l)F + Pt1F 7 EOS 6330 GO TO 6P3 EOS P M P 8» ,0 0 ie e i*t -,«8 0 1 E -0 6 *T **2 +,5 a 7 7 E -1 0 *T **3 EOS 6350 PMP9«-,6816+, *T -.? E -0 b *T **2 +, E T **3 EOS 6360 PMP86*CPMP9-PMP6)+DF+PMP8 EOS 6370 GO TC/ 600 EOS P H P 9 * ,301517*T,3 2 7 ie -0 6 *T *+ 2 +, E "1 0 *T **3 EOS 6390 PMP10b-, *T -, 1963E-06* T * *2 +, E -10 * T**3 EOS 6400 PMP86*(PPP10-PhP9)*OF+PMP9 EOS 6010 GO TO 800 EOS P M P l.-«.7 9 q +,«5 7 3 E -0 3 *T +,a E -0 6 *T ** O E -1 0 *T **3 EOS 6430 PM P2« ,6332E -B 3*T+.!6A 6E -eb *T i**2-,a632e -10*T*«3 EOS 6440

86 PMPB0* (PMP?-PMP1)*DF + PMPi EOS 6450 GO TO 800 EOS PMP?* - 4, 19H E -0 3 M +.3 b 4 6 E -0 6 *T **2 -, E -1 0 *T **3 EOS 6470 P M P 3« E -cj 3 *1 +, E -0 6 *T ** E -1 0 *T a*3 EOS 6480 PMPB8* (PMP3-PMF2)6UF + PMP? EOS 6490 GO TO 600 EOS P M P 3*-2, E -P 3 *T +, E -0 6 *T *» E -1 0 *T **3 EOS 6510 P M P «*-t *.5 B 4 le -0 4 *T +,P E -0 6 «r**2 -, E -1 0 *T **3 EOS 6520 PMP00r(PHP«-PMP3)*OF+PMP3 EOS 6533 GO TO 603 EOS PMP4« ,56 4iE -04*T E 06*Titr*a-,27 4eE-10*T»»3 EOS 6550 P» P 5» * E -0 3 *T +, E -0 6 *T ** E -11»T**3 EOS 6560 PMP 88 (PMP5-PMP4)*0F + PMP4 EOS 6570 GO TO 600 EOS P M P 5 s E -0 3 *T +,i0 3 3 E -0 6 *T ** E -lt*t **3 EOS 6543 P M P b « e *T +,3 9 l? E -0 6 *T **2 -.l8 7 7 E -l«*t **3 EOS 6603 POP 88 * CPmpb-POP5 )* 0F + PmP5 EOS 6610 GO TO 600 EOS P M P 6«3,6 3 6-, *T +, E -0 6 *T **2 -, E -1 0*T *«3 EOS b 633 PM P7«4,678-,k>02193*T+,4675E-06*T**2-.221E-10*T**3 EOS 6640 PMP88stP*P7-PHP6)*0F+PMPb EOS 6653 GO TO 8O0- EOS PMP7s , *T E -06*T **2-.221E -10i*T **3 EOS PMP8«.165JE + 01-,3754E"03*Ttf*l +. 16O6E-06* T* * E - U * T * *3 EOS 6660 PMP88* IPmpb-P mpj)*df + PMP7 EOS 6690 GO TO 800 EOS P M P 8 * E , E -0 3 *T **t+ ' E -0 6 *T ** E «ll*t **3 EOS P[lP9 =, t'-0<l*T+, 7308E-07*T«i* E -1 2 *T **3 EOS 6720 P0P88* (PMP9-PMP6)*0F+PMP8 EOS 6730 GO TO 800 EOS PM P9t.l?01E+01+,4513E-0a*T+.7308E-07«T**2+,2018E-12*T*«i3 EOS b7 50 P M P l0 s,7 P? 7 t.5 1 fc le -0 3 *T -,3 P 3 4 E -0 7 *T ** E -U *T **3 EOS 6760 PMP?.6 * (Pf'Pl0-PMP9) *DF+PMP9 EOS GO TO 800 EOS PMP8fi» ( , * *0 ** 2 +, *0**3) + ( T * ( -, 172BE-04- EOS 6790 X.2J3E -k}4*d+.4169e-0'.l*o **2-.18E-05*D**3)) EOS 6800 B0P IF(BUPN.GT,8,) P U B 6 * 8, EOS 6810 PMPiPMPfib-( (PMPBU-PMP55)* ( (B.-B U H N )/3 )) EOS PJ0 IF (P M P.IT.0.) PMP.0.0 EOS 6830 PMP«10*»PMP EOS 6840 PMP*PMP*(eiMP+ZP0SMP**2+B2MP*ZP0SMP+MPHETU EOS 6850 IF(TMXXMP,EQ,TmINMP)GO TO 820 EOS 6860 XXXXX* (T-TMINMP)/ (TMAXMP-TMINMP) EOS 6870

87 PMPi PMP*OMIN1 U, D 0 f XXXXX) EOS IFITAUMP.GT.0.0.ANO. (TC R T M P -P M O T (M,U ).IE.0.0) EOS 6890 X PMR.pMp* (1,-OEXP((TCRTMP-PMOT(M,U)/TAUMPn EOS 6900 PMP»PMP*l.0l325E+0b EOS 6910 GO TO 202 EOS P MP e 0,0 EOS 6930 GO TO 202 EOS CONTINUE EOS 6950 SP ( 5 ) *SP(5) EOS 6960 IFLAG*2 EOS 6970 IF(P2.GE.P1J I p L A G 1 EOS 6960 GO TO 3080 EOS 6990 *3060 POLO * P (Mr U EOS 7P00 IF(U (M,L )/(R H O U (M #L )»V FU (M,l)),G E.(U M E L T(K )*1000,0+HFUSE(K) EOS O )) EOS 7020 t GO TO 3070 EOS 7030 PAVG * P(M,L) EOS 7040 IF (1U0L0(m, l ),E O,2 ) GO TO 3020 EOS 7050 luolo(m.l) «2 EOS 7 C 60 GO TO 3020 EOS U (M,U»U(M,u-HFUSE(K}*RHOUCM,L)»VFUCMf L} EOS 7090 IUOL 0 (M, L)* 1 EOS 7090 GO TO 3020 EOS 7100 C EOS 7110 C DETERMINE AVERAGE PRESSURE FOR CURRENT ITERATION EOS 7120 C EOS IF (IP T F L.E O.l) go TO 3120 EOS 7140 PR 1 * SP 13) EUS 7153 IF(P(M,L).LT,PO LO ) GO TO 3090 EOS 7160 ITFLG «1 EOS 7170 IF (IFLAG,HE,8) GO TO 3100 EOS I i f f l m EOS 7190 PAvr,«PCM,L) EOS 7200 GO TO 31 6M EOS ITFLG*2 EOS 7220 IF (IFLAG.E0.2) PR 1»0,99999 EOS J J * 1 EOS 7240 PPX*P(M,L) EOS PAVG»POLD+(PPX -P0L0)*PR1 EOS 7260 GO TO 3160 EOS IFCITFLG.EQ.2) GO TO 3140 EOS 7280 IFCP(M,L).GE.PAVG) GO TO EOS IFCJJ.GE.10) GO TO 3250 EOS 7300

88 EOS 7310 PR1*PRI*0.5 EOS 7320 GO TO 3110 EOS IF (P (M,U,L E,P A V G ) GO TO 3200 EOS 7340 GO TO 3130 EOS 7350 C EOS C ADJUST THE DENSITIES EOS 7370 C EOS A«EA «0.5 * ( (Z (M + l.l + l > - 2 C M, U ) * ( R ( M + i,l ) - R ( M,L M» - EOS (R(M +i,l + t)-r (M f t ) j ) EOS 7400 CENTRO «0,2 5 *(R (M,l+ 1 ) *R (M+ I, L* 1) *R (M M,L ) R (M,U J EOS 7410 VOLUME» AREA * CENTRO EOS RH0NA(H,L)*RHQNA0CH,U*(P»V5 *8 1 NA/(P0N A (K ) * 1. E93 *1.)**B 2N A EOS RH0SSCM,l.)*»H05S0(M,U*CPAVG *H /t B0SS K ) * 1. E9) i,)** B 2 S 5 EOS 7440 IE (RHOSSC M,L).NE.0,0.AND.HHO NA (M,U.Nt,0.0) GO TO 3100 EOS 7460 IF (HHOS3(M,L).EQ.0.H) GO TO 3170 EOS 7460 R H O U (H,U» massu(m,u/(v0lum E-HA35S5CM,L)/RH0SS(M,U) EOS GO TO 3190 EOS RHOU(M,U)«HASSU(M,U/tVOLUMe-MASSNA(Mf L )/R H O N A (M,U ) EOS 7490 GO TO 3190 EOS R H O U IM,U *m>ssu(h,l)/cvolume-massnacm,u/rhonach,l)-masssscm,u/ EOS RH0S3(M,L)) EOS KEUVOL M,U«RHOCRT/RHOU M,U EOS 7530 VFIJ(M,u)= (MASSU CH,U/WHOU(H,L))/'VOLUME EOS 7540 IP (IAOJ.EG.t 1) GO TO 3010 EOS 7550 IF C IIF E L.E H.l) GO TO 3250 EOS 7560 IPTFLM EOS 75/0 GO TO 3020 E C EOS 7590 C CHECK FOR CONVERGENCE EOS 7600 C EOS IF (OABS(P(M,U-PAVG ),UE,SP(4)*PAVG ) GO TO 3250 EOS 7620 IF (*MM.GE.98J PRINT M,L, REDVOL(H, L), VFU(M, L)# MMM EOS FORMAT ( ' AT ME3 H PG INT'( 2 l 4, f RED. VOL.,'1 P E 9.3,» VOL. FEOS R A C, *, ' 1 PE9,3 r ' NO, OF ITERATIONS *,114) EOS 7650 IF CHMM.GE.98J PRINT 3 220,UCM, L J, THETA(M, L5, POLO, PAVG, EOS P (M,L ), IFLAG EOS FORMAT (5E1 4,6,16) EOS 7680 MMM«MMM+1 EOS 7690 IF (MMM.GE.10i) GO TO 3230 EOS 7700 POLD»PAVG EOS 7710 GO TO 3100 EOS PRINT 3240 EOS 7730

89 3200 FORMAT(1H, 'NOT CONVERGEO IN 100 ITERATIONS') EOS IF(H M M.G t.t) GO TO 3260 EOS 7750 P (M,U PAYS _ ECS 7760 RO TO 3270 EOS P (M,U = C P A vr,*p (M,U )/2. EOS CONTINUE EOS 7790 C EOS 7800 C CALCURATE ENEHGY IN MOLTEN FUEL EOS 7810 C > EOS 7820 IF(THETA(M,L).LT.TMELT(K)) GO TO 3276 EOS 7830 IF(THF.TA(M,L).G T.TM ELT(K)M.) GO TO 3270 EOS S P (U )B S P (in *(H F U S E (K ) )*M A S5U (M,L)*6*28316* EOS (THETA(M,L)-TMELT(K)) EOS 7860 GO TO 3276 EOS SP(m*SP(li)+MASSU(M,L)*6,28318«(HFUSE(K)t(THETA(M,L)-TMELT(K)) EOS /?,?87) EOS CONTINUE EOS 7900 C. E O S 7910 C CALCULATE WMA7 FOR TIME STEP CONTROL EOS 7920 C EOS 7930 IFUFLAG.E0.2) GO TO 3320 EOS 7900 WCC*KHCCHT*MASSZRCM,L) /MASSUCM,L) EOS 7950 IF (VFNA(MiL).bO.0.0) GO TO 3280 EOS 7960 WOO*KMOCHT»MASSNA(MjL)t (MASSU(M,L)*RHONA(M,L)**2) EOS 7970 GO TO 3290 EOS *00*0,0 EOS WEE» WH ON A(M, l ) / (3.5 9 * P(M,L) B0 N A(K)»1,E9) EOS 8000 IF(REOVOL(M,l).GE,1.0) GO TO 3300 EOS 8010 WAAsP8P*l,E-10 EOS 8020 WHB»P6b*(PAA*(a,89*REDVOL(M( L )-9,6 7 )*, /R E D V O U M,L )* *4 ) EOS 8030 GO TO 3310 EOS WAAsPCC*l,E-10 EOS 8050 Wfibr (3, E E E )* 1,9fc-10*PCC**2 EOS C2?*(P(M,U*WAA-weB*wCC)/(Cl,«W89*WD0i>HEE)*RM0NEWCM,L)*«2) EOS 8070 GO TO 3330 EOS C? 2«( ,9256E-7*THETA(M,L))* CPCM,L)/ (RHONEW(M,L)* EOS THF.TA(M,L)))**2 EOS 8100 C 22*0M A Xl(C 22,l.D -5) EOS COMPUM,/(R H 0 U (M,U *C 2 2 ) EOS 6120 IF (VENA (MrL ),N E,0.) COMPNA.l.52E-11/RH0NA(M,L) EOS 8130 IF(VFSS(M( L ).N E.0,0 ) C0MPSS»0,E-12/RHOSS(M,L) EOS 8100 C 2 2» l, / (RHONEW(M,L)*(COMPU*VFU(M,L)*COMPNA»VFNA(M,L)+CQMPSS* EOS VFSS(MrL ) n EOS 8160

90 WW.C23*COEUT/l,2)**?/AREA + a.p*oabs(rhoncw(m,u3*oelvcm»l)) EOS 8 J70 IF CWW.UE.5PC8) J GO TO 3349) EOS 8180 SP(9)*RW EOS 8190 ISP(a)*rt EOS 8200 IS P (93 *L EOS GO TO 9000 EOS 8220 C EOS 8230 C EQUATION 08 STATE FOR REFLECTOR REGIONS EOS 8240 C EOS IF (VFN* (M, L1.N E.0. 0) COMPNAtj,5?E-n/RH0NA(M,L) EOS e260 IF (V F S 5 (M» U.N E,0.0 ) COHPSS*a.E-l?/RHOSSCM,L) EOS 8270 IF (VFU(M,L), ME.0.0 ) C0MPF«2.5E-11/KH0'J(M,L) EOS 6280 COMPaG«CUMPNA*VFNA CH,L)+CONPSS*VFSS cm, L) 8C0MPF*VFU(M,U EOS 6290 DRUH«(RHONEw{M,l)-RHUO(M,L))/RROO(Mf L) EOS 83P0 WWsa,0.OAR5(HhONENCMrU)*OELV(M,L)) ECS 8310 IF(ORQH,GT,EPSI10(K)) GO TO 40(0 EOS 8320 P ( M, L ) r I), 0 EOS 0333 GO TO 4020 ' EOS 83a P(M,L)«CDROH-EPSI10(R))/COMPAG EOS 8350 IF (P (N f l ). L T. l. E - 9 ) P (M,L )*0.0 EOS 8360 AREA 0.S*((7tM*l#L+l)-Z(M,U)*(R(M*i,LJ-R(M,t + n ) - EOS 8370 l ( P ( " M, L * l } - R ( M, L 3 ) * ( 2 ( M + l,l ) - Z ( M f L + l)) 3 EOS 8390 WWswWf(OELT/1, 2 ) * * 2 / (AREA*«HOOCM,L)aCOHPAG) EOS IF(ww.LE,SP(B3) GO TO 4030 EOS 6400 SP(8)*W'W EOS 6010 ISP(6)«H EOS 8420 IS P ( 9 ) *L EOS GO TO 9000 EOS CONTINUE EOS CONTINUE EOS M 2, IMAXP1 EOS 8470 DU 9020 L 2,JHAXPl EOS 8490 IF ( M ( M, L ).E U. l.and, KTVAPP.EQ.3) P (M, L) «P (M,1)* 1, E+6 EOS 6490 IF (KT ( M,L ),E 0.1.AND. KTVAPP.EQ.4) P(M, L)«P(M #L ) * 1. E*6 EOS 8500 PATZR(m,L3*P(M,L) EOS 6510 IF ( P ( M,L ).L T t SP(13)) P (M,L )«0.0 EOS 8520 IF ( KT CM t L),LE. 4,0R, KT(M,t),GE. 6 ) GO TO 9020 EOS 8530 P(H,L 3 P(M,L) * l.e + 6 EOS CONTINUE EOS 8550 ENO EOS 8560

91 REFERENCES 85

92 LIST OF REFERENCES 1. La Marsh, John R., In tro d u c tio n to Nuclear E ngineering. Addison- Wesley P u b ls ih in g Company, Reading, M assachusetts, Koch, C.J., Loewenstein, W.B., and Monson, H.O., "Hazard Surronary Report E B R -II," Addendum to Hazard Summary Report Experimental R e a c to r-ii, Jackson, J.F., and N icholson, R.B., "VENUE-II: An LMFBR Disassembly Program," ANL-7951, Bethe, H.A., and T a it, J.H., "An Estim ate o f the Order o f Magnitude o f the Explosion When the Core o f a Fast Reactor C o lla p se s," UKAEA-RHM956/113, Jackson, J.F., and Eaton, A.M., "P re s s u riz a tio n Rate E ffe c ts in Irra d ia te d Core Disassembly C a lc u la tio n s," Transactions o f the American N uclear S o c ie ty, V o l. 22, 1975, pp Brook, A.J., "Some P re lim in a ry C onsiderations R elating to an. E q u a tio n -o f-s ta te fo r Irra d ia te d Nuclear F u e l," Nuclear S afety 13, No SRD R 13, Bogensberger, H.G., "C a lc u la tio n s o f the E ffe c ts o f F ission Gas in an LMFBR, fo r the A nalysis o f an Unprotected Overpower T ra n s ie n t," KFK 1990, EVR 4875e, P re p rin t, Schw arzblat, M., "An E quation-o f-s tate fo r Mixed Oxide Fast Reactor F u e ls," PhD D is s e rta tio n, U n iv e rs ity o f A rizona, Jackson, J.F., Stevenson, M.G., M archaterre, R.H., Avery, R., and O tt, K.O., "Trends in LMFBR H ypoth e tica l-a ccid e n t A n a ly s is," March, G abelnick, S.D., and Chasanov, M.G., "A C alculated Approach to the E stim ation o f Fuel and F ission - Product Vapor Pressures and O x id a tio n S ta te s to 6000 K," ANL-7867, Bruber, E.E., "Fission-G as E ffe c ts in the A nalysis o f LMFBR H ypothetical A ccid e n ts," Argonne N ational Laboratory, In tr a - Laboratory Memo, March 28, Gruber, E.E., "C a lc u la tio n s o f T ra n sie n t Fission-Gas Release from Oxide F u e ls," ANL-8143,

93 MacExan, J.R., and Lawson, V.B., "G rain Growth in S intered S io xid e : I I, Columnar Grain G rowth," Journal o f the American Ceramic S o c ie ty, V o l. 45, No. 1, January 1962, pp Sesonske, Alexander, Nuclear Power P lant Design A n a ly s is, Technical In fo rm a tio n C enter, O ffic e o f In fo rm a tio n Services United States Atomic Energy Commission, Oak Ridge, Tennessee TID-26241, N ic h o ls, F.A., and Warner, H.R., "S w e llin g and Gas-Release Models f o r Oxide Fuel Rods (LWBR Development P rogram )," Fast Reactor Fuel Element Technology, Farmakes, Ruth e d.. In te rs ta te P rin te rs, D a n v ille, I l l i n o i s, 1971, pp Lambert, J.D.B., Neimark, L.A., Murphy, W.F., and Dickerman, C.E., "Performance o f Mixed-Oxide Fuel Elements - ANL E x p e rie n c e," Fast Reactor Fuel Element Technology, Farmakes, Ruth e d.. In te rs ta te P rin te rs, D a n v ille, I l l i n o i s, 1971, pp O krent, D., Lecture Background Notes on F ort Reactor Fuel. Element B e h avio r, Thomas, Garry R., and F ie ld, John H., "Oxide Fuel Behavior During T ra n sie n t Overpower C o n d itio n s," Fast Reactor Fuel Element Technology, Farmakes, Ruth e d.. In te rs ta te P rin te rs, D a n v ille, I l l i n o i s, 1971, pp Eaton, Andrew M., "A F ission-p ro d uct Pressure Model fo r Fast Reactor Dissassembly C a lc u la tio n s," Master o f Engineering P ro je c t, Brigham Young U n iv e rs ity, 1975.

94 AN IMPROVED FISSION PRODUCT PRESSURE MODEL FOR USE IN THE VENUS-II DISASSEMBLY CODE Ray L. Jensen Department o f Mechanical Engineering MS Degree, A p ril 1976 ABSTRACT This th e s is presents an improved fis s io n product pressure model fo r in c lu d in g the e ffe c ts o f the fis s io n product pressures in the VENUS-II disassem bly c a lc u la tio n s. The pressures o f the noble gases, the a lk a li m etals and rem aining fis s io n products are pre dicte d a n a ly tic a lly as a fu n c tio n o f tem perature, fuel-sm ear d e n s ity and and burnup. A p p ropria te re d u ctio n s are made on these pressures to account fo r the a x ia l dependence o f the fis s io n product re te n tio n. The p re s s u riz a tio n o f each o f the mentioned groups is in it ia t e d by a separate preset tem perature c r it e r io n. Delay times and exponential p re s s u riz a tio n ra te s are included to model the p re s s u riz a tio n o f each group. A lso, included in th is model is an o p tio n to release the fis s io n p roduct pressures o ver a tem perature range. Sample cases are ran to demonstrate the use and f l e x i b i l i t y o f the re p o rt. The re s u lts in d ic a te th a t th is new model w ill be a useful to o l in im proving the e v a lu a tio n o f fa s t re a c to r disassembly c a lc u la tio n s. COMMITTEE APPROVALS: