TURKISH ATOMIC ENERGY AUTHORITY
ÇEKMECE NUCLEAR RESEARCH AND TRAINING CENTER
IS T A N B U L - T U R K E YTechnical Report No: 37
DENSITY SEARCH CALCULATIONS
FOR THE SILISIDE FUELS
Mehmet Hulusi TURGUT
Nuclear Engineering Departm ent
December 1986
TURKISH ATOMIC ENERGY AUTHORITY
ÇEKMECE NUCLEAR RESEARCH AND TRAINING CENTER
IS T A N B U L ■ T U R K E YTechnical
Report
No: 37
DENSITY SEARCH CALCULATIONS
FOR THE SILISIDE FUELS
Mehmet Hulusi TURGUT
Nuclear Engineering Department
December 1986
A B B R E V I A T I O N S
HEU : Highly Enriched Uranium Fuel (ca, 90% U-235)
LEU : Low Enriched Uranium Fuel (less than 20% U-235)
BOC : Beginning of Cycle
MOC : Middle of Cycle
EOC : End of Cycle
PPF : Power Peaking Factor
FE23 : Fuel Element at core position 23
CE55 : Control Element at core position 55
IE64 : Irradiation Element at core position 64
SR-1 : Safety Rod-1
CR-1 : Control Rod-1
Ö Z E T S İ L İ S L İ Y A K I T L A R İÇ İ N Y O Ğ U N L U K T E S B İ T İ H E S A P L A R I T R - 2 r e a k t ö r ü n ü n " K a l p D ö n ü ş t ü r m e " h e s a p l a r ı n d a k u l l a n ı l m a k ü z e r e bir d e n g e k oru h e s a p m o d e l i g e l i ş t i r i l m i ş t i r . M o d e l iki b o y u t l u h e s a p l a r ı n b a ş l a n g ı c ı n d a , d ü ş ü n ü l e n y akıt y e r d e ğ i ş t i r m e ş e k l i n e göre, t a h m i n i yanma o r a n l a r ı n ı n v e r i l m e s i e s a s ı n a d a y a n m a k t a d ı r . Bu s u r e t l e d e n g e d u r u m u n a y a k l a - ş m c a y a k a d a r y a p ı l a c a k i t e r a s y o n sayı s ı a z a l m a k t a ve d o l a y ı s ı y l a b i l g i s a y a r z a m a n ı n d a n bü y ü k ö l ç ü d e (% 70 ka d a r ) k a z a n ç s a ğ l a m a k t a d ı r . M o d e l e b i r d e n fazla yakıt y e r d e ğ i ş t i r me ş e m a s ı n ı n v e r i l e b i l m e s i ayrı bir a v a n t a j ı n ı t e ş k i l e t m e k t e d i r . Bu m o d e l k u l l a n ı l a r a k T R - 2 r e a k t ö r ü için a l ı n m a s ı d ü ş ü n ü l e n d ü ş ü k z e n g i n l i k l i s i l i s l i y a k ı t l a r ı n y o ğ u n l u ğ u a r a ş t ı r ı l m ı ş t ı r . B u n u n için k r i t e r o l a r a k y ü k s e k z e n g i n l i k t e k i y a k ı t l a r a yakın bir p e r f o r m a n s s a ğ l a n m a s ı e sas a l ı n m ı ş t ı r . D e n g e k o r u n a i l â v e e d i l e c e k Be y a n s ı t ı c ı l a r ı n k â l b ö mrü ve a t ı l a n y a k ı t l a r d a k i y anma o r a n ı n a olan t e s i r l e r i i n c e l e n m i ş tir.
S U M M A R Y
D E N S I T Y S E A R C H C A L C U L A T I O N S F O R T H E S I L I S I D E F U E L S
An e q u i l i b r i u m core c a l c u l a t i o n a l m o d e l has been d e v e l o p e d and used for the " C o r e C o n v e r s i o n " c a l c u l a t i o n s of the T R - 2 re a c t o r . The m o d e l is based on a b u r n u p g u e s s at the b e g i n n i n g of the 2D c a l c u l a t i o n s a c c o r d i n g to the fuel s h u f f l i n g s t r a t e g y . T h i s r e d u c e s the n u m b e r of i t e r a t i o n s u n t i l the core r e a c h e s to the e q u i l i b r i u m s i t u a t i o n and so the c o m p u t e r time d e c r e a s e s c o n s i d e r a b l y (up to 70%). A n o t h e r a d v a n t a g e of this m o d e l is the p o s s i b i l i t y of g i v i n g m o r e than one fuel s h u f f l i n g s c hemes.
T h i s new m o d e l is used for the d e n s i t y s e a r c h c a l c u l a t i o n s of the LEU s i l i s i d e fuel w h i c h will h ave s i m i l a r p e r f o r m a n c e s as the HEU fuel. The e f f e c t of a d d i t i o n a l Be r e f l e c t o r s on the c ore l i f e t i m e and the d i s c h a r g e b u r n u p l e v e l s h ave been d i s c u s s e d .
CONTENTS
Page SUMMARY
1. INTRODUCTION 1
2. CALCULATIONAL TOOLS 2
3. EQUILIBRIUM CORE PHILOSOPHY 2
A. CALCULATIONS 4
5. CONCLUSIONS 8
REFERENCES 10
TABLES
Table 1 : Group structure used in 2D calculations H
Table 2 : Fuel shuffling paths for TR-2 studies H
Table 3 : The average deviations in the thermal fluxes 1^
Table 4 : PPF's for different cases 1^
FIGURES
Fig. 1 : X-Y picture of the equilibrium core 13
Fig. 2 : Burnup distribution (%) at the EOC for HEU core 1^
Fig. 3 : Burnup distributions (%) at the EOC for LEU cores 1^
Fig. 4 : EOC excess reactivities for different fuel types 15
Fig. 5 : EOC excess reactivities for Case-2 15
Fig. 6 : EOC excess reactivities for Case-3 16
Fig. 7 : EOC excess reactivities versus U density 16
Fig. 8 : Thermal flux distributions for Case-1 17
Fig. 9 : Thermal flux distributions for Case-2 17
Fig. 10: Thermal flux distributions for Case-3 16
1. I N T R O D U C T I O N
Th e aim of this s t udy is to find the o p t i m u m d e n s i t y and the d e s i g n of the LEU fuel for the T R - 2 r e a c t o r . F r o m the p r e v i o u s c a l c u l a t i o n s ( l ) and the W o r l d ’s t e n d e n c y ( 2 , 3 , 4 , 5) t o w a r d s the s i l i s i d e fuel, it is c o n c l u d e d that s i l i s i d e w o u l d be the best o p t i o n for the T R-2 r e a c t o r . The ma i n a d v a n t a g e of the s i l i s i d e fuel is the p o s s i b i l i t y of g i v i n g s i m i l a r p e r f o r m a n c e s as the HEU fuels w i t h o u t any m o d i f i c a t i o n in the fuel e l e m e n t d esign. T h i s m e a n s m i n i m u m p r o b l e m s w i l l a r r i s e in t h e r m o h y d r a u l i c s and s a f e t y b e c a u s e of the c h a n g e of fuels.
Our c o n s t r a i n t s for the c o n v e r s i o n of the T R - 2 r e a c t o r f r o m the use of HEU fuel to LEU fuel are:
1. Sa m e c ore c o n f i g u r a t i o n in both cases, 2. No c h a n g e in the fuel e l e m e n t design, 3. S ame fuel s h u f f l i n g s chemes,
4. N e u t r o n i c and t h e r m a l - h y d r a u l i c p a r a m e t e r c h a n g e s (i.e., c h a n g e s in s a f e t y m a r g i n s ) must be w i t h i n a c c e p t a b l e limits.
O b j e c t i v e s of this c o n v e r s i o n s t udy is:
1. To a c h i e v e the same core l i f e t i m e as the HE U fuel,
2. EOC k - e f f e c t i v e va l u e must not be less than the
v a l u e o b t a i n e d in HEU case,
3. To r e a c h the m a x i m u m p e r m i s s a b l e b u r n u p l e v e l s in the d i s c h a r g e d fuel e l e m e n t s ,
4. M i n i m u m p o s s i b l e d e c r e a s e in the t h e r m a l flux w h i c h f u l f i l s the a b o v e r e q u i r e m e n t s .
?
2. C A L C U L A T I O N AL T O O L S
T w o d i m e n s i o n a l d i f f u s i o n - d e p l e t i o n c o d e G E R E B U S ( 6 ) is used for the c a l c u l a t i o n s . 5 g r o u p c r o s s - s e c t i o n s w h i c h a r e g e n e r a t e d at A N L for H E U and L E U f u e l s are used in the c a l c u l a t i o n s . T h e g r o u p s t r u c t u r e is g i v e n in T a b l e 1. T h r e e
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d i f f e r e n t fuel d e n s i t i e s , 3.5, 4.0, 4.5 g r / c m , h a v e b e e n us e d in the c r o s s - s e c t i o n g e n e r a t i o n for the U ^ S i2 fuel. T h i s is the d e n s i t y r a n g e for the LE U fuel w h i c h w i l l f u l f i l our r e q u i r e m e n t s a c c o r d i n g to the p r e v i o u s c a l c u l a t i o n s . M O C c r o s s - s e c t i o n s are used for all c a s e s s t u d i e d w h i c h g i v e r e a s o n a b l e v a l u e s for t his t ype of c o m p a r i s o n c a l c u l a t i o n s . S c a t t e r i n g is a s s u m e d to be on l y to one l o w e r g r o u p s i n c e the g r o u p s are q u i t e broad. T h e s a m e e x t r a p o l a t i o n l e n g t h is us e d in all c a s e s , s i n c e it is not v ery s e n s i t i v e to e i t h e r e n r i c h m e n t or u r a n i u m l o a d i n g for the p l a t e - t y p e c o r e s . In L E U fuel it w i l l be a l i t t l e bit h i g h e r than H E U w h i c h w i l l c a u s e a b o u t 2 - 3 % i n c r e a s e in the e x c e s s r e a c t i v i t y . S i n c e we d o n ’t k n o w the e x a c t v a l u e for LE U fuel, the o n e for H E U is used to be on the s a f e r side.
3. E Q U I L I B R I U M C O R E P H I L O S O P H Y
A f t e r the f i r s t few l o a d i n g s of the r e a c t o r s , it is a d v a n t a g e o u s to go to an e q u i l i b r i u m c o r e s i n c e m o s t of the f uel e l e m e n t s r e a c h to c e r t a i n b u r n u p l e v e l s and b e c a u s e of t h a t it is no m o r e p o s s i b l e to a c h i e v e the d e s i r e d c y c l e length by r e f u e l l i n g a few e l e m e n t s in the core. An e q u i l i b r i u m c o r e is d e f i n e d as the c o r e that is r e a c h e d a f t e r i n f i n i t e t ime of l o a d i n g s of the r e a c t o r a c c o r d i n g to a f i x e d s h u f f l i n g s c h e m e . By t h i s way it is p o s s i b l e to fi n d an o p t i m u m l o a d i n g p a t t e r n t hat g i v e s the d e s i r e d c y c l e l e n g t h and d i s c h a r g e b u r n u p level.
3 T h e s a m e c o r e l o a d i n g and th e s a m e s h u f f l i n g s c h e m e w h i c h is g i v e n in the d e s i g n s t u d i e s ( 7 ) h a v e b e e n u s e d in the c a l c u l a t i o n s . In F i g u r e 1 the 2D r e p r e s e n t a t i o n of th e T R - 2 r e a c t o r is s h o w n . S i d e p l a t e s h a v e b e e n d e f i n e d as s e p a r a t e r e g i o n s in t h i s m o d e l . Al l r o d s a s s u m e d to be o u t in the c a l c u l a t i o n s s i n c e t h i s is a c o m p a r i s o n s t u d y b e t w e e n H E U and LE U . T h e o u t - i n s h u f f l i n g p a t t e r n for the s t a n d a r t f u e l e l e m e n t s is g i v e n in T a b l e 2. A f r e s h f u e l e l e m e n t is p l a c e d at p o s i t i o n F E 3 6 in the B O C and a f u l l y - b u r n e d f u e l e l e m e n t is d i s c h a r g e d f r o m p o s i t i o n F E 5 3 at the E O C . T h e b u r n c y c l e n u m b e r a s s o c i a t e d w i t h a p a r t i c u l a r p o s i t i o n r e p r e s e n t s th e n u m b e r of c y c l e s th a t an e l e m e n t at t h a t p o s i t i o n h a s b e e n b u r n e d at t h e EOC. F o r the c o n t r o l e l e m e n t s the s h u f f l i n g p a t t e r n F r e s h C E 5 5 C E 3 A C E 4 3 + C E 6 3 D i s c h a r g e is u s e d . C o n t r o l e l e m e n t s a r e s h u f f l e d a f t e r e v e r y A c y c l e , t h a t m e a n s o n e f r e s h c o n t r o l e l e m e n t r e m a i n s A c y c l e s in e a c h p o s i t i o n and a f t e r 16 c y c l e s t h e y are d i s c h a r g e d . A l t h o u g h t h e s t a n d a r t f u e l e l e m e n t s r e m a i n 17 c y c l e s in the c o r e b e f o r e t h e y a r e d i s c h a r g e d , t h e y h a v e n e a r l y t h e s a m e burttUp l e v e l w i t h the c o n t r o l e l e m e n t s , s i n c e the c o n t r o l e l e m e n t s a l w a y s r e m a i n in the i n n e r p o s i t i o n s w h e r e the n e u t r o n f l u x is h i g h . F o r the i r r a d i a t i o n e l e m e n t it is a s s u m e d t h a t 3 0 % b u r n e d e l e m e n t is p l a c e d in the b e g i n n i n g of e v e r y c y c l e . By t h i s w a y of h a n d l i n g of the i r r a d i a t i o n e l e m e n t , th e c a l c u l a t i o n t i m e s h o r t e n e d e x t e n s i v e l y . T h i s t y p e of e q u i l i b r i u m c o r e c a l c u l a t i o n s a r e too m u c h t i m e c o n s u m i n g . F o r e x a m p l e , one s u c h c a l c u l a t i o n for t h e T R - 2 r e a c t o r t a k e s a b o u t 1 8 - 2 0 h o u r s c o m p u t e r t i m e s t a r t i n g f r o m the f r e s h l o a d i n g u n t i l it r e a c h e s to e q u i l i b r i u m d i s t r i b u t i o n , in V A X - 1 1 / 7 5 0 w h i c h is a v a i l a b l e at our c e n t e r . T h i s is very i n c o v e n i e n t for our c o m p u t e r , s i n c e m a n y r e s t a r t s a r e n e c e s s a r y , w h i c h w i l l c a u s e a d d i t i o n a l l o s s of
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c o m p u t e r and data r e a d j u s t m e n t time. In o rder to s o l v e this p r o b l e m an a c c e l e r a t i o n t e c h n i q u e has been i n t r o d u c e d to the G E R E B U S code. In this m e t h o d a b u r n u p guess has be e n m a d e a c c o r d i n g to the s h u f f l i n g schemes. It is s u f f i c i e n t to give only the n u m b e r d e n s i t y d i s t r i b u t i o n of the U - 2 3 5 i s o t o p e , si n c e it is the d o m i n a t i n g i s o t o p e in our case. Th e n u m b e r d e n s i t i e s of the fresh fuel can be used for the o t h e r i s o topes. Af t e r the first few b u r n u p st e p s all the i s o t o p e s r e a c h to their n o rmal c o n c e n t r a t i o n values. If one has no idea of the b u r n u p d i s t r i b u t i o n of the e q u i l i b r i u m core, a G E R E B U S run for one cy c l e can be made, s t a r t i n g f r o m the fr e s h l o a d i n g and the a v e r a g e b u r n u p level of the co r e d u r i n g one c y c l e can be found. Th i s value, then, can be used in the e s t i m a t i o n of the b u r n u p l e v e l s of e ach e l e m e n t , by m u l t i p l y i n g the n u m b e r of c y c l e s that each e l e m e n t has be e n r e m a i n e d in the core. The b u r n u p l e v e l s are p r o p o r t i o n a l to the cy c l e l e n g t h and the e n r i c h m e n t , so a small p r o g r a m has been w r i t t e n to find the r e a s o n a b l e g u e s s e s for the c a s e s that we have studied. By u s i n g this d e s c r i b e d m e t h o d the c o m p u t a t i o n time r e d u c e s a b out three times, w h i c h e n a b l e s us one run in one day.
4. C A L C U L A T I O N S
The d e t a i l e d core g e o m e t r y w h i c h is used in the c a l c u l a t i o n s is given in F i g u r e 1. The w a t e r r e f l e c t o r t h i c k n e s s was c h o s e n to be 20 cm . 64 x 5 5 m esh p o i n t s w e r e taken. Th e e x t r a p o l a t i o n l e n g t h t a ken to be 7. 7 4 6 cm.
F i r s t HEU p e r f o r m a n c e for e q u i l i b r i u m co r e is i n v e s t i g a t e d . The BOC e x c e s s r e a c t i v i t y is found to be 7273 pern and af t e r 150 M W D 1s o p e r a t i o n EOC e x c e s s r e a c t i v i t y is 50 3 5 pcm. T h e b u r n u p level in the d i s c h a r g e d fuel e l e m e n t is 5 0 . 8 5 % (the limit of the fuel f a b r i c a t o r s is 50%). T h e b u r n u p d i s t r i b u t i o n for the EOC is given in F i g u r e 2. The b u r n u p l e v e l
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in th e d i s c h a r g e d c o n t r o l e l e m e n t is h i g h e r t h e n the s t a n d a r t e l e m e n t in t h i s run, but in r e a l i t y it w i l l be l o w e r th a n t h i s v a l u e , s i n c e all r o d s a s s u m e d to be out in t h i s c a l c u l a ti o n . If we s i m u l a t e the CR 2 i n s e r t i o n , t h e n the f lux in p o s i t i o n C E 5 5 w i l l be d e c r e a s e d and the b u r n u p w i l l be l e s s for th e c o n t r o l e l e m e n t in t h i s p o s i t i o n d u r i n g 4 c y c l e s . T h i s w i l l c a u s e a f e w p e r c e n t d e c r e a s e in the b u r n u p l e v e l of th e d i s c h a r g e d c o n t r o l e l e m e n t .
T h e e x c e s s r e a c t i v i t i e s for the L E U f u e l s at the B O C a r e 4 0 1 1 , 64 7 2 , 8 2 4 2 pern and at t h e E O C ar e 2126, 4937, 6 9 3 3 p e m for t h e d e n s i t i e s 3.5, 4.0, 4 . 5 g r / c m , r e s p e c t i v e l y . It c a n be s e e n t h a t the l o s s of r e a c t i v i t y for 15 0 MWDs o p e r a t i o n of th e T R - 2 r e a c t o r d e c r e a s e s in L E U fuel c o m p a r e d to H E U f u e l and t h i s d e c r e a s e is p r o p o r t i o n a l to the fu e l d e n s i t y . T h i s c a n be e x p e c t e d s i n c e the U - 2 3 5 c o n t e n t w i l l be h i g h e r for h i g h e r d e n s i t i e s , so the b u r n u p w i l l be less. T h i s c a n a l s o be s e e n in th e b u r n u p l e v e l s of the d i s c h a r ged L E U f u e l s : 4 5 . 5 5 % for t h e f u e l d e n s i t y 3.5 g r / c m ^ , 4 0 . 0 8 %
^ 3
for 4 . 0 g r / c m , 3 5 . 7 8 % for 4 . 5 g r / c m . T h e b u r n u p d i s t r i b u t i o n s for t h e s e t h r e e c a s e s a r e g i v e n t o g e t h e r in F i g u r e 3.
S i n c e the c y c l e l e n g t h a n d the E O C e x c e s s r e a c t i v i t y a r e the m a i n o b j e c t i v e s , it is no t n e c e s s a r y to m a t c h the B O C e x c e s s r e a c t i v i t y of the H E U fuel.
F r o m t h i s f i r s t s e r i e s of c a l c u l a t i o n s it is s e e n that w i t h t h e L E U f u e l d e n s i t y of 3. 5 g r / c m , it is not p o s s i b l e to m a t c h the s a m e c y c l e l e n g t h and th e s a m e E O C e x c e s s r e a c t i v i t y w i t h th e H E U fuel, w i t h o u t any c h a n g e in the c o r e d e s i g n . 4 . 0 g r / c m d e n s i t y s e e m s to f u l f i l ou r r e q u i r e m e n t s a n d w i t h h i g h e r d e n s i t i e s l o n g e r c y c l e l e n g t h s can be e x p e c t e d . S i n c e we w o u l d a l s o l i k e to r e a c h the l i m i t i n g d i s c h a r g e b u r n u p l e v e l for the L E U fuel, a fe w m o r e c a l c u l a t i o n s h a v e b e e n m a d e for l o n g e r c y c l e l e n g t h s . In F i g u r e 4 the EOC e x c e s s r e a c t i v i t i e s and the d i s c h c a r g e b u r n u p l e v e l s of H E U a n d L E U f u e l s h a v e b e e n c o m p a r e d for d i f f e r e n t c y c l e l e n g t h s .
6
O n e run has been made for 3.5 g r/cm , since the EOC e x c e s s r e a c t i v i t y is m uch lower then HEU even for 150 M W D1s .
In or d e r to see the e f f e c t of a d d i t i o n a l Be r e f l e c t o r s 2 d i f f e r e n t s e r i e s of c a l c u l a t i o n s have been c a r r i e d out. First, the r e p l a c e m e n t of A1 blocks, w h i c h are d e s i g n e d for i r r a d i a t i o n p u r p o s e s and not used in the small c o r e up to now, w i t h Be b l o c k s is c o n s i d e r e d . T his i n c r e a s e s the B O C e x c e s s r e a c t i v i t y in HEU core 961 pern, in LEU co r e 908, 848,
3
810 pem for the fuel d e n s i t i e s 3.5, 4.0, 4.5 g r / c m , r e s p e c t ively. S i m i l a r c u r v e s like F i g u r e 4 have been o b t a i n e d for EOC excess r e a c t i v i t i e s . T h i s is s h own in F i g u r e 5 w i t h the d i s c h a r g e b u r n u p levels.
A n o t h e r trial is m ade by 4 a d d i t i o n a l Be r e f l e c t o r s
to the core p o s i t i o n s 37, 47, 57, and 67 in a d d i t i o n to
r e p l a c e m e n t of A1 blocks. The a d d i t i o n a l Be r e f l e c t o r s i n c r e a s e d the e x c e s s r e a c t i v i t i e s for HEU and L E U c o r e s by d i f f e r e n t a m o u n t s as e x p e c t e d and e n a b l e d us to go to h i g h e r c y c l e l e n g t h s and to the d e s i r e d d i s c h a r g e b u r n u p l e v e l s (See F i g u r e 6 ). T h i s is e s p e c i a l l y i m p o r t a n t in LEU fuel, s i n c e the d i s c h a r g e b u r n u p l e v e l s for 150 MWDs o p e r a t i o n are q u i t e lo w e r than the limit g iven by the fuel f a b r i c a t o r s .
The v a r i a t i o n of EOC e x c e s s r e a c t i v i t i e s for 150 M W D s o p e r a t i o n a g a i n s t the LEU fuel d e n s i t y are g iven t o g e t h e r for
the 3 ca s e s (2 Al, 2 Be, 6 Be) in F i g u r e 7. No t e that the
c u r v e s for HEU are plotted for fixed fuel d e n s i t y (P = 0 . 6 9 2 2 g r / c m ^ ) in or d e r to see for w h i c h d e n s i t y and for w h i c h ca s e we can r e a c h the HEU p e r f o r m a n c e . It can be s een that the
3 3
fuel d e n s i t i e s 4.0 g r / c m for c a s e -1 , 3.84 g r / c m for case-2 3
and 3.4 g r / c m for c a s e - 3 can f u lfil our o b j e c t i v e s .
T h e t h e r m a l flux d i s t r i b u t i o n s , in the core and in the s u r r o u n d i n g w a t e r boxes, for HEU and LEU f u els are g i v e n in
F i g u r e s 8 , 9, 10 for the 3 cases. It can be seen that the
t h e r m a l flux d e c r e a s e s in g o i n g from HEU c ore to LE U c o r e
7
and t h i s d e c r e a s e is m o r e for h i g h e r fuel d e n s i t i e s . So it is p r e f e r a b l e to c h o o s e the l o w e s t p o s s i b l e d e n s i t y for the L E U fuel w h i c h will f u l f i l our r e q u i r e m e n t s . T h e d e c r e a s e s ** in t h e r m a l f lux are gi v e n in F i g u r e 1 1 for the c a s e -1 . For the o t h e r c a s e s s i m i l a r d e v i a t i o n s are o b s e r v e d . T h e decreases in t h e r m a l flux is f o r t u n a t e l y m u c h l ess in the w a t e r b o x e s t h e n the core. T h i s is a f a v o r a b l e c o n d i t i o n s i n c e the i r r a d i a t i o n s t a k e p l a c e in wa t e r boxes. T h e a v e r a g e d e v i a t i o n s in the c o r e and in the w a t e r b o x e s are g i v e n t o g e t h e r in T a b l e 3 for the 3 cases.
T h e P P F s w h i c h are i m p o r t a n t f r o m the s a f e t y p o i n t of view, are c a l c u l a t e d for the d i f f e r e n t c a s e s and g i v e n t o g e t h e r in T a b l e 4. T h e PPFs d e c r e a s e w h e n we c h a n g e H E U fuel to L E U and they decrease m o r e w i t h the i n c r e a s e in the fuel d e n s i t y for the same c y c l e length. T h e d e c r e a s e , in r e a l i t y , is not b e c a u s e of the c h a n g e of the fuel or the d e n s i t y , but b e c a u s e of the d e c r e a s e in the d i s c h a r g e b u r n u p l e v e l w h e n we c h a n g e to L E U fuel. For the same d i s c h a r g e b u r n u p we h a v e a l m o s t the s ame P P F for b oth H E U and L E U fuels. P P F s increase w h e n the d i f f e r e n c e in the b u r n u p l e v e l s b e t w e e n the l o a d e d and the d i s c h a r g e d fuel is h i g h e r . It a l s o d e p e n d s on the s h u f f l i n g p a t t e r n and the c ore c o n f i g u r a t i o n . T h e a d d i t i o n of Be b l o c k s a l s o r e d u c e s the P P F s since t hey c a u s e a f l a t t e n i n g in the f orm of the flux d i s t r i b u t i o n . F o r the t h i r d c a s e the i n c r e a s e s in P P F s are because of the 30 M W D ' s a d d i t i o n a l o p e r a t i o n of the r e a c t o r w h i c h c a u s e an i n c r e a s e in the d i s c h a r g e b u r n u p levels.
T h i s p r e l i m i n a r y c a l c u l a t i o n s s h o w us the o p t i m u m d e n s i t i e s for LE U fuel lies b e t w e e n 3 . 7 - 4 . 2 g r / c m for the T R - 2 r e a c t o r . A n o t h e r c r i t e r i a to c h o o s e the o p t i m u m d e n s i t y for the L E U fuel is the price. T h i s will d e p e n d on t h e fuel f a b r i c a t o r s and the d e m a n d for a s p e c i f i c d e s i g n . So it w i l l be b e n e f i c i a l to c h o o s e a d e n s i t y in t his range, w h i c h the f u e l f a b r i c a t o r s a l r e a d y p r o d u c e s . A f t e r h a v i n g the p r i c e s for d i f f e r e n t fuel d e n s i t i e s it is p o s s i b l e to m a k e a n o t h e r
set of optimisation calculations depending on TL/MWD.
, HEU , LEU
9 ~ 9
8
5. C O N C L U S I O N S
The r e s u l t s of these p r e l i m i n a r y c a l c u l a t i o n s can be s u m m a r i s e d as follows:
1. S i n c e this is a c o m p a r i s o n study b e t w e e n HEU and LEU fuels, the r e p r e s e n t a t i o n of the e q u i l i b r i u m c o r e e x p l a i n e d in this r e p o r t is s u f f i c i e n t . But for the f inal c a l c u l a t i o n s it is b e t t e r to s i m u l a t e the c o n t r o l rod i n s e r t i o n and r e p r e s e n t a t i o n of the i r r a d i a t i o n e l e m e n t m u s t be m o d i f i e d .
2 . Th e s h u f f l i n g s c h e m e s for s t a n d a r t and c o n t r o l e l e m e n t s used in this s t udy are qu i t e good, s i n c e P P F fs are low and the d i s c h a r g e b u r n u p l e v e l s for s t a n d a r t and c o n t r o l e l e m e n t s are a l m o s t the same.
3. T h e excess r e a c t i v i t y n e e d e d at BOC for a c e r t a i n c y c l e l e n g t h is less in LE U core than HEU and it d e c r e a s e s by i n c r e a s i n g the fuel densi t y . So it is not n e c e s s a r y to m a t c h the BOC excess r e a c t i v i t y of the HEU core to a c h i e v e the same c y c l e length.
4. T h e d i s c h a r g e b u r n u p l e v e l s d e c r e a s e by the increase in the fuel d e n s i t y for the same c y c l e length, but t hey remain c o n s t a n t for the same fuel type even if one p l a c e s a d d i t i o n a l Be r e f l e c t o r s to the core.
5. T h e b u r n u p l e v e l s in the d i s c h a r g e d L E U f u e l s can be i n c r e a s e d a c c o r d i n g to the f a b r i c a t i o n l i m its. T h i s can be a c h i e v e d by a d d i t i o n a l Be r e f l e c t o r s w i t h o u t any c h a n g e in the core design.
6 . R e p l a c e m e n t of w a t e r bo x e s a n d / o r A1 b l o c k s w i t h Be b l o c k s i n c r e a s e s the c y c l e l e n g t h a n d / o r it a l l o w s us to go to l o wer fuel d e n s i t i e s for the same c y c l e l e n gth.
9
7. T h e d e c r e a s e in the t h e r m a l f lux i n c r e a s e s w i t h the i n c r e a s e of the f u e l d e n s i t y , so it is p r e f e r a b l e to c h o o s e t h e f u e l d e n s i t y as low as p o s s i b l e w h i c h w i l l f u l f i l our r e q u i r e m e n t s •
8 . F o r t u n a t e l y , the d e c r e a s e in t h e r m a l f l u x is m u c h l e s s in the w a t e r b o x e s t h a n the core.
9. A d d i t i o n a l Be r e f l e c t o r s d o e s n ’t c h a n g e the a v e r a g e d e v i a t i o n s in the t h e r m a l f l u x e s for all the c a s e s .
10. T h i s p r e l i m i n a r y c a l c u l a t i o n s s h o w e d t h a t the d e n s i t y of the L E U fu e l w h i c h g i v e s a b o u t the s a m e performance
3
as the H E U f u e l is a b o u t 4.0 g r / c m w i t h o u t any c h a n g e in the c o r e . 11. A n o t h e r c r i t e r i a to c h o o s e the o p t i m u m d e n s i t y for t h e L E U f u e l is the price. It w i l l be b e n e f i c i a l to c h o o s e 3 a d e n s i t y in the r a n g e 3 . 7 - 4. 2 g r / c m w h i c h the fu e l f a b r i c a t o r s a l r e a d y p r o d u c e s .
12. P P F ’s d o e s not d e p e n d m u c h on the f u e l t y p e or the d e n s i t y of the L E U fuel. It d e p e n d s on the d i s c h a r g e b u r n u p l e v e l , f u e l s h u f f l i n g p a t t e r n and the c o r e c o n f i g u r a t i o n .
13. A d d i t i o n of Be b l o c k s d e c r e a s e s the P P F ’s. In c o n t r a r y , l o n g e r c y c l e l e n g t h s c a u s e i n c r e a s e in P P F ’s.
14. D u e to no c h a n g e in the fuel e l e m e n t d e s i g n t h e r e w i l l a r r i s e no a d d i t i o n a l s a f e t y p r o b l e m s .
10 R E F E R E N C E S (1) T . A l d e m i r , M . H . T urgut, M . M . B r e t s c h e r , J .L .S n e l g r o v e , "A F e a s i b i l i t y S t u d y C o n c e r n i n g the C o n v e r s i o n of the T R- 2 R e a c t o r f rom U s i n g H i g h l y E n r i c h e d U r a n i u m to L i g h t E n r i c h e d U r a n i u m " , Ç N A E M - R - 2 1 7 (1982). (2) A . T r a v e l l i , "The S t a t u s of the R E R T R P r o g r a m : O v e r v i e w , P r o g r e s s and Plans", ANL, U.S . A . , I n t e r n a t i o n a l M e e t i n g on R e d u c e d E n r i c h m e n t for R e s e a r c h and T e s t R e a c t o r s , O c t o b e r 14-16, 1985, P etten, The N e t h e r l a n d s .
(3) J .L .S n e l g r o v e , G . L . H o f m a n , and G .L .C o p e l a n d , " I r r a d i a t i o n P e r f o r m a n c e of R e d u c e d - E n r i c h m e n t F u e l s T e s t e d U n d e r the U.S. R E R T R P r o g r a m " , ANL, U .S.A., I n t e r n a t i o n a l M e e t i n g on R e d u c e d E n r i c h m e n t for R e s e a r c h and T e s t R e a c t o r s , O c t o b e r 14-16, 1985, P etten, The N e t h e r l a n d s . (4) M . H r o v a t , H . W . H a s s e l , and E . W e h n e r , " S t a t u s of Development and I r r a d i a t i o n P e r f o r m a n c e of A d v a n c e d P r o l i f e r a t i o n R e s i s t a n t MTR F uel at N U K E M " , N U K E M GmbH, W . G e r m a n y , I n t e r n a t i o n a l M e e t i n g on R e d u c e d E n r i c h m e n t for R e s e a r c h and T e s t R e a c t o r s , O c t o b e r 14-16, 1985, Pe t t e n , N e t h e r l a n d s . (5) Y . F a n j a s , P h . D e w e z , "MTR F uel at C . E . R . C . A . : S t a t u s of D e v e l o p m e n t - O c t o b e r 1985", C . E . R . C . A . , F r a n c e , I n t e r n a t i o n a l M e e t i n g on R e d u c e d E n r i c h m e n t for R e s e a r c h and T e s t R e a c t o r s , O c t o b e r 14-16, 1985, P etten, N e t h e r l a n d s . (6 ) M . C o n s o l e , A . D a n e r i , and E . S a l i n a , "EREB U S : A M u l t i g r o u p D i f f u s i o n D e p l e t i o n P r o g r a m in Two D i m e n s i o n s " , F N - E- 8 8 (FIAT, 1967). (7) Ş.Erk, et al., " P r o j e c t du R e a c t e u r TR-2 5MW de Ç e k m e c e " , C e n t r e d ' E t u d e s de G r e n o b l e R e p o r t C E N - G P i - S E R E G 10 1 2
11
Ta b l e Is Group s t ructure used in 2D c a l c u l a t i o n s
Gr o u p No Upper Energy of the Group. {eV}
1 l . O O O O x l O7
2 8 . 2 0 8 5 x l 0 5
3 5 . 5 3 0 9 x l 0 3
4 1. 8 5 5 0
5 6 . 2 4 9 3 x l 0 _1
T a b l e 2: Fuel S h u f f l i n g Paths for TR-2 S t u d i e s (Refer to Fig. -1 for Fuel E l e m e n t P o s itions) Burn Cycle (Stage) Nu m b e r s Fuel Elem e n t P o s i t i o n " O u t s i d e - I n " 1 FE36 2 FE25 3 FE7 5 4 F E6 6 5 FE56 6 FE46 7 FE7 3 8 FE74 9 FE24 1 0 FE23 1 1 FE35 1 2 FE65 13 FE33 14 FE45 15 FE44 16 FE54 17 FE53
12
T a b l e 3: The a v e r a g e d e v i a t i o n s in the t h e r m a l f l u x e s
Average deviations in the thermal fluxes(%)
OPERATION [m w d]
In the core In water boxes
CASE LEU 3.5 gr/cm3 LEU 4.0 gr/cm3 LEU 4.5 gr/cm3 LEU 3.5 gr/cm3 LEU 4.0 gr/cm3 LEU 4.5 gr/cm3 2 A1 150 1 1 . 6 23.3 32.0 0.7 2.9 4.4 2 Be 150 1 1 . 6 23.4 32.1 0 . 8 3.0 4.6 6 Be 180 14.4 26.5 35.3 2 . 1 4.9 6 . 8 T a b l e 4: P P F ' s for d i f f e r e n t c a s e s CASE OPERATION [m w d] HEU LEU 3.5 gr/cm3 LEU 3 4.0 gr/cm LEU 4.5 gr/cm3 2 A1 150 1.972 1.829 1.773 1.734 2 Be 150 1.962 1.820 1.765 1.727 6 Be 180 2.155 1.938 1.859 1.806
N u m b e r o f m « sh p o in ts 13
14
m
W7777
/ W . t W . ^ft////
/ / / / » * / /W777/
^ fcWt.V’V 4 2 2 / p i B U t V ' . ^ 2 2 / ! P f ^ B l r o W / 73 2.1 3 3 u 2 9 . 0 3 n 3 7 . 9 0kl.
4? 55 5#.*5 ci 5 6 3 3Vt
3 2.6 0 «•«f 44. <o sw 47.*1 PfZ^-H
74 2J.S9 tsM
»5 3 2 .1 2 45 4 1 ' H 55 Cl 3 4 .W 75 3 . 2 6m
3 .4 2 w 1&.92 56 1 s.6 o <4 1 2 .1 9 P i X f c U c V VFigure 2: Burnup distribution (%) at the EOC for HEU core
y/M
/ *«- - y / H.cW'/
72 7
/ B t y / V w ic . / [/ / B e / / / , BWc-ln/
//»<•//
/////,
1 1 *777/7
' 7
“ -• • S 3 2 ^ 1 0.
or'
3 3 .9 3 2 9 6 4 26 .31 “’ « . 3 1 _ l l i i 45.55" 4o.og 35.79 ‘ *5*.S8 *19.14 16.50 1 4 .5 4 111 2 3 .8 7 2 0 .4 7 1 2 .2 6 2 4 . *9 — 22î_âİL *»w 3 9 .9 2 3 4 .9 3 3 1 . 0 S4 4 2 .8 8 3 7 . 6 2 3 3 .5 3 w 3 3 . 6 5 33 .17 32.31 ’ 4 2 1 .4 9 I t . 5 8 I 6 .4 0 15 5 .7 5 4 .9 5 4 .9 2 55 2 8 .V 0 2 5 .0 1 2 2 .1 4 45 3 6 . 9 3 3 2 .1 6 2 3 . 5 7 551S.7S 1J.4-3 _ M L c$ 3 1 .2 9 2 7 .2 2 Z 4 .1 3 »» 8 .3 0 7 .1 1 6 .2 4 s s l w â o fr 2 .S 9 2 . 2 5 <•< . 1 6 .9 3 4 4 -5 5 1 2 .7 * 56 1 3 9 9 1 2 .0 1 1 0 .5 5 ai « . 9 4 9 - 3 9 8 . 2 5 P I X b u cV \ 1) LEU 3.5 gr/cm3 2) LEU 4.0 gr/cm3 3) LEU 4.5 gr/cm3R
O
-E
O
C
C
P
C
M
3
R
O
-E
O
C
CPCM3
15Figure 4: EOC excess reactivities for different fuel
*) Discharge burnup
types
*) Discharge burnup
R
O
-E
O
C
C
P
CM
3
16 -*) Discharge burnupFigure 6: EOC excess reactivities for Case-3
U D E N S I T Y [
c m 3J
17 a. 290" 2. 071 2. 3 0 6 ’1 De Be De De De De 2. 124 2. 2İB '' 2. 0 5 0 a. ı s ı ' 1' 2. 0 0 8 3. 6 7 0 2. 60 7 3. 710 4. 6 4 3 4. 604 4. 150 2. 404 3 2 0 5 3. 65 4 2. 376 3. 2 0 0 3. 9 5 6 3 0 3 0 3. 5 3 ? 2. 192 3. 33 7 3. 4 0 5 2. 06 7 2. 76 7 3. 414 3. 20 7 3. 05 5 1. 9 3 0 3. 2 0 6 3. 3 5 0 1. 0 3 6 2. 4 3 ? 3. 0 1 0 2 0 7 9 2. 6 9 3 1. 732 3. 1 0 ? 4. 3 0 5 2. 7 7 5 3. 8 ? 3 4. 764 4. 9 6 0 6. 0 6 6 2. 6 3 0 3. 9 5 2 4. 34 4 2. 461 3. 3 5 6 3. 9 5 0 4. 145 5. 744 2. 3 9 0 3. 9 8 3 4. 121 2. 123 2. 07 7 3. 35 4 3. 527 5. 24 4 2. 0 0 0 3. 804 3. 95 5 1. B73 2. 524 2. 9 1 4 3. 0 7 5 4. 861 1. 0 6 3 3. 6 7 2 3. 95 7 2. 52 0 3. 4 4 2 4. 137 3. 7 9 3 3. 27 7 2. 35 0 3 6 0 2 3. 9 1 0 2. 304 2. 9 5 7 3. 464 3. 36 6 2. 0 5 5 2. 173 3. 61 6 3. 701 2. 01 1 2. 514 2. 9 2 2 2. 90 2 2. 4 3 ? 1. 90 4 3. 43 7 3. 544 1 . 77 4 2. 193 2. 53 2 2. 5 5 ? 2. 136 1. 704 3. 30 7 2. 94 7 2. 6 0 7 3. 0 9 9 3. 051 2. 601 2. 6 9 2 2. 937 A! 2. 4 5 ? 2. 7 5 0 2. 7 5 3 2. 37 2 A1 2. 71 6 2. 7 0 6 2. 141 2 361 2. 3 0 0 2. 0 6 2 2. 592 2. 67 9 1. 90 7 2. 0 7 ? 2. 107 1. 8 3 6 2. 505 1. 271 3. 0 1 6 4. 2 0 0 5. 190 5. 0 0 0 4. 0 3 9 2. 777 1. 160 1. 2 7 2 2. 9 7 0 4. 2 2 0 5. 120 5. 021 4. 0 0 8 2. 79 0 1. 176 1. 21 2 2. 0 3 7 3. 7 6 0 4. 00 4 4. 7 1 0 3. 7 7 3 2. 65 4 1. 127 1. 169 2. 72 3 3. 77 4 4. 577 4. 501 3. 60 5 2. 55 8 1. 09 4 1) HEU 2) LEU 3.5 gr/crn3 3) LEU 4.0 gr/cm3 4) LEU 4.5 gr/cm3
Figure 8: Thermal flux distributions for Case-1
2. 236^ 2. 256*. 2. i 7 2 v 2. 10 0* Be Be De De De De 2. 0 2 6 2. 0 8 2 2. 0 1 0 1 . 9 7 0 3 6 1 2 2. 64 3 3. 64 5 4. 52 6 4 501 4. 061 2. 367 3. 2 3 ? 3. 6 0 2 2. 330 3 147 3. 06 6 3. 756 3. 466 2. 1 5 ? 3. 29 5 3. 4 3 ? 2. 0 3 5 ? . 716 3. 3 3 ? 3. 21 0 2. 99 4 1 . 9 0 2 3 160 3 515 1. 0 0 7 2. 39 4 2. 94 4 2. 0 1 ? 2. 64 0 1. 70 6 3. 0 7 2 4. 410 a. 8 0 9 3. 0 7 0 4. 7 1 0 4. 90 5 6. 0 3 3 2. 64 7 3. 9 0 2 4. 372 a. 4 7 3 3. 3 4 0 3. 9 1 3 4. 100 5. 716 2. 404 4. 0 1 5 4. J 40 P. 134 2. 06 4 3. 31 7 3. 47 0 5. 2 2 0 2. 100 3. 034 3 9 0 2 1. 8 0 2 2. 51 3 2. 0 0 2 3. 0 4 3 4 04 1 1 . 0 73 3. 701 4. 102 2. 544 3. 500 4. 150 3. G05 3. 3 4 0 2. 30 5 3 741 4. 0 5 7 2. 3 1 6 3. 01 1 3. 40 0 3. 37 9 2. 90 6 2. 100 3. 7 5 0 3. 031 2. 0 1 7 560 2. 9 3 6 2. 91 4 2. 40 2 1. 91 2 3 561 3 6 6 5 1 7 9 5 2. 231 2. 543 2. 570 2. 172 1. 706 3. 424 2. 94 3 2. 73 3 3. 162 3. 10 ? 2. 6 4 0 2. 69 6 2. 91 3 Be 2. 4 9 2 2. 0 0 5 2. 0 0 5 2. 4 04 De 2. 700 2 75 0 2. 166 2. 4 0 ? 2. 425 2. 00 6 2. 56 3 2. 63 3 X. 924 2. 121 2. 146 1. 0 5 2 2. 463 1. ? 9 6 3. 0 3 0 4. 4 7 3 5. 3 2 0 5. 194 4. 21 7 2. 004 1. 106 1. 291 3. 0 0 3 4. 40 7 5. 2 4 2 5. 130 4. 102 2. 7 7 ? 1 176 1. 22 4 2. 0 2 ? 4. 135 4. 921 4. 0 3 0 3. 926 2. 6 4 ? 1. 141 1. 170 2. 70 4 3. 9 3 0 4. 6 0 ? 4. 6 0 0 3. 7 5 ? 2. 543 1. 102 1) HEU 2) LEU 3.5 gr/cm3 3) LEU 4.0 gr/cm3 4) LEU 4.5 gr/cm3
18 7 ^ 7 a. o b<« 3. 005* 1. 947*) B?
I
f t p Be B e Be Be 1 . 0 7 4 1. 931 1 . 0 7 2 1. 0 2 0 3. 39 5 5. 6 U 3. 7 3 2 4. 63 6 4. 73 9 4. 1 72 2 3 6 0 3 0 6 5 3. ^79 5. 2£}7 -3 1 19 3. 03 6 3 001 3 461 2. 107 3. 1 1 1 3. 2 2 2 1. 97 6 2. 6 6 0 3. 2 0 6 3. 221 2. 96 5 1 0 4 3 2. 905 3. 105 1. 74 6 2. 3 3 7 2. 0 0 0 2. 0 0 0 2. 590 1 . 6 4 5 2. 091 4. 31 0 2. ^35 4. 0 9 0 5. 100 5. 4 12 6. 106 2. 76 5 3 92 7 4. 5 4 0 2. 50 5 3. 4 10 4. 1 16 4. 329 5. 69 5 2 44 1 3. 92 / 4. 00 9 2. 139 2. 901 3. 441 3. 63 5 5. 160 2 111 3 732 3. 041 1. 0 7 5 2. 52 7 2. 96 2 3. 140 4. 77 3 1. 0 70 3. 592 A. 221 *9. 73 9 4. 0 4 0 4. 9 5 3 4. 310 3. 061 2. 6 0 9 3. 0 0 0 A. I P B 2. 4*;:? 3. 331 3. 95 4 3. 72 3 3. 2 3 0 2. 33 7 3 0 5 0 3 074 2. JOB P. 795 3. 2 0 5 3. 175 2. 72 0 2. 021 3. 63 0 3. <73 1 . 0 * 6 7. 41 5 2. 01 7 2. 70 0 2. 35 9 1. 79 3 3. 47 5 3. 2 6 2 3. 2 2 5 3. 0 0 7 3. 79 0 3. 20 7 3 014 3. 179 Be 2. 0 6 3 3. 3 0 3 3. 291 2. 0 1 5 Be 2. 971 2. 9 7 8 2. 4 50 2. 771 2. 00 2 2. 40 0 2. 77 6 2. 0 3 7 2. 167 2. 42 9 2. 453 2. 110 2. 67 5 1. 569 3 e e o 3. 6 3 0 1. 44 5 1 . 53 5 3. 7 4 5 Be Be Be Be 3. 531 1. 43 2 1. 44 3 3. J)8? 3. 2 9 5 1 . 3 5 3 1. 300 3. 2 ? 8 3. 131 1. 3 0 0 1) HEU 2) LEU 3.5 gr/cm3 3) LEU 4.0 gr/cm3 4) LEU 4.5 gr/cm3Figure 10: Thermal flux distributions for Case-3
- 0 . 70 7 1 2 3 3. 136?> 6. 079'1 Be Be Be Be Be Be - 2. 56 9 0. 6 1 0 3. 0 4 2 0. 431 5. 0 2 7 9. 51 0 11. 567 23. 0 0 2 31. 6 7 9 13. 67 7 25. 55 7 3 4 . 3 0 1 1 4 . 7 9 0 26. 47 5 35. 183 16. 63 0 20. 601 37. 45 9 14. 07 0 26. 534 35. 244 0. 034 17. 72 3 27. 767 - 1 . 562 2. 39 9 5 37 6 0. 9 3 3 6. 0 2 5 7. 0 0 6 11. 7 2 3 24. 0 43 32. 97 4 13. 7 7 2 26. 107 35. 167 16. 9 2 5 29. 6 0 2 30. 0 2 5 16. 43 7 2 8 . 9 0 0 30. 0 0 2 5. 31 7 13. 560 19. 0 6 2 7. 143 20. 6 2 0 27. 100 - 0 70 4 3. 75 5 7. 0 9 0 0. 9 9 6 6. 457 1 0 . 4 4 5 0. 563 20. 106 20. DOG 14. 0 7 6 26. 7 6 2 36. 3 0 2 16. 2 7 2 27. 371 30. 00 7 11. 2 4 3 23. 495 32. 534 12. 0 0 7 25. 576 34. 03 7 7. 00 7 17. 241 2 7. 73 3 - 0 . 40 0 4 504 0. 102 0. >424 5. 517 9. 140 A1 0. 461 20. 2 7 0 29. 0 2 7 11. 2 5 7 23. 7 0 7 32. 9 0 7 9. 7 4 8 21. 907 30. 9 5 2 0. 0 1 0 20. 67 5 27. 41 2 A 1 - 0 . 8 7 5 3. 703 6. 9 3 9 - 0 . 0 5 5 4. 6 0 0 8. 0 0 0 0. 62 7 5. 761 9. 7 4 0 1. 3 7 7 7. 467 11. 0 2 3 1. 51 0 7. 50 5 11. 94 6 Î . 163 7. 129 11. 40 5 0. 77 2 6. 573 10. 74 0 - 0 . 4 43 4. 457 7. 0 7 6 - 1 . 3 0 0 2. 0 3 6 5. 74 0 1) LEU 3.5 gr/cm3 2) LEU 4.0 gr/cm3 3) LEU 4.5 gr/cm3
