after processing. Within a short time, a very high radiation
-
86-
Table 11.22. U232 penalty.
Parts of U232 Penalty in dollars per million parts per gram of
of uranium total uranium
Source: Eighty-Ninth US Congress (1 966)
.
level builds up due to fast decay of Th228 from U232 into Ra224 (the half-life of Th228 is 1.9 years). Refabrication of larger quantities of U223 within ten days after processing would, in principle, be possible without gamma shielding, but this re- quires a smooth production sequence (Baier 1974).
Calculations of the ~ 2 3 2 buildup in the HTR utilizing the thorium fuel cycle indicate U232 concentrations of up to 500 ppm in the case of repeated recycling of the fissile fuel (Baier 1974). Since this concentration level is sufficient to require shielding, this is the range of U232 concentrations shielding in HTR refabrication plants has to be designed for.
The buildup of U232 takes place by means of essentially three reactions:
(1) Th232 (n,2n) Th231 25 8 - Pa231 ( n , ~ ) Pa232 6.34 MeV
(2) U233 (n,2n) U232 6 MeV
Due t o t h e r e l a t i v e l y h i g h t h e r m a l c a p t u r e c r o s s s e c t i o n o f
Figure 11.17. Buildup of U232 in the first (R1) and second (R2) rows of blanket elements as well as for the radial blanket (R averaged over R1 and R2), in the thorium blankets.
t o HTR r e p r o c e s s i n g a n d r e f a b r i c a t i o n p l a n t s , t h e U232 c o n c e n t r a - t i o n s o f b o t h b l a n k e t s r e m a i n w i t h i n t h e r a n g e s t i p u l a t e d f o r HTR r e f a b r i c a t i o n p l a n t s ( 5 0 0 ppm-1000 ppm).
The r e s i d e n c e t i m e o f t h e r a d i a l b l a n k e t s i s t h u s n o t l i m i t e d by t h e U232 b u i l d u p . The f i n a n c i a l p e n a l t y i s a l s o k e p t w i t h i n l i m i t s , d u e t o t h e r e l a t i v e l y low U232 c o n c e n t r a t i o n b u i l t u p
i n t h e b l a n k e t ( s e e T a b l e 1 1 . 2 2 ) . 1 I . l O . c . I n f l u e n c e o f Pa233
The b u i l d u p o f U233 t a k e s p l a c e v i a t h e d e c a y o f t h e i n t e r - m e d i a t e d e c a y p r o d u c t Pa233. T h i s p r o c e s s i s s i m i l a r t o t h e b u i l d u p o f Pu239 v i a t h e d e c a y o f t h e i n t e r m e d i a t e p r o d u c t Np239.
U 2 3 8 ( n , y ) 92U239 0 - 0 -
92 2 3 . 5 min 9 3 Np239 2 . 4 day;94 Pu239
Th232 ( n , y ) gOTh233
. -
6- 6-90 22 min 91 P a 2 3 3 27.4 d a y < 9 2 U233
The b a s i c d i f f e r e n c e b e t w e e n t h e s e two c h a i n s i s t h e r e l a t i v e l y l o n g h a l f - l i f e o f 27.4 d a y s f o r P a 2 3 3 , a s compared t o 2.4 d a y s f o r Np239. T h i s h a l f - l i f e c a u s e s h i g h e q u i l i b r i u m c o n c e n t r a t i o n s o f Pa233 t o b u i l d u p , m a i n l y i n t h e case o f h i g h power d e n s i t i e s .
C o n s i d e r a b l e r e a c t i v i t y i n s e r t i o n m u s t t h e r e f o r e b e e x p e c t e d , a f t e r r e a c t o r s h u t d o w n . T h i s r e a c t i v i t y i n s e r t i o n m u s t b e com- p e n s a t e d f o r by a d d i t i o n a l c o n t r o l r o d s . I f t h o r i u m i s u s e d i n t h e c o r e z o n e s , t h i s e f f e c t becomes a c o n s i d e r a b l e p r o b l e m (see t h e f o l l o w i n g s e c t i o n ) .
When t h o r i u m i s u s e d i n t h e r a d i a l b l a n k e t , t h e Pa233 d e c a y i s o f m i n o r i n f l u e n c e s i n c e , f i r s t l y , o n l y r e l a t i v e l y s m a l l e q u i l i b r i u m c o n c e n t r a t i o n s a r e b u i l t u p , b e c a u s e o f t h e low power d e n s i t y ( o n l y a b o u t 22 k g o f P a 2 3 3 f o r t h e Tho2 a n d
~ h ~ b l a n k e t s ) a n d , s e c o n d l y , t h e P a 2 3 3 i s l o c a t e d i n a r e a c t o r r e g i o n o f r e l a t i v e l y s m a l l r e a c t i v i t y w o r t h . The maximum r e a c t i - v i t y w o r t h o f t h e a b o v e amount o f P a 2 3 3 i n t h e b l a n k e t s w a s c a l - c u l a t e d a s 3 . 0 % i n k e f f , by means o f two k
e f f c a l c u l a t i o n s f o r
which Pa233 was assumed t o be e q u i v a l e n t t o U233. T h i s i n c r e a s e
F i g u r e 1 1 . 1 8 . R a d i a l d e p e n d e n c e o f t h e s o d i u m v o i d e f f e c t A K v ( R ) f o r U 0 2 a n d Tho2 r a d i a l b l a n k e t s . P e r t u r b a t i o n c a l c u l a t i o n f o r a s o d i u m - f r e e 1 - l i t e r b u b b l e . The 1 0 % r i s e o f t h e s o d i u m v o i d c o e f f i c i e n t i n core z o n e C Z ~ i s o f r e l a t i v e l y l i t t l e i m p o r t a n c e , s i n c e t h e u n c e r t a i n t i e s i n d e t e r m i n i n g t h e s o d i u m v o i d e f f e c t a r e r e g a r d e d t o b e w i t h i n t h i s r a n g e . The i n c r e a s e i s t h e r e f o r e w i t h i n t h e e x p e c t e d un- c e r t a i n t y l i m i t s . T h e D o p p l e r c o e f f i c i e n t c o u l d n o t b e i n v e s t i - g a t e d h e r e d u e t o a l a c k of n u c l e a r d a t a . However, i t c a n b e d e d u c e d f r o m Wood a n d D i s c r o l l ( 1 9 7 3 ) t h a t t h e r e i s l i t t l e d i f - f e r e n c e b e t w e e n t h e D o p p l e r c o e f f i c i e n t s o f t h e t w o b l a n k e t con- f i g u r a t i o n s .
1 1 . 1 7 . THORIUM I N THE FBR CORE REGION
The i n f l u e n c e o f t h o r i u m i n t h e FBR c o r e z o n e s o n t h e g l o b a l b r e e d i n g r a t i o a n d r e a c t i v i t y c o e f f i c i e n t s h a s b e e n e x a m i n e d i n d e t a i l i n s e v e r a l s t u d i e s ( L o e w e n s t e i n a n d O k r e n t 1 9 5 8 ; O k r e n t , C o h e n , a n d L o e w e n s t e i n 1 9 6 5 ; H a n k e l e t a l . 1 9 6 2 ; L o e w e n s t e i n
a n d B l u r n e n t h a l 1 9 6 5 ; A l l e n , S t o k e r , and C a m p i s e 1 9 6 6 ; S o f e r e t a l . 1 9 6 3 ) . I n t h i s i n v e s t i g a t i o n , i t h a s a l r e a d y b e e n shown i n
S e c t i o n I I . 9 . b . t h a t u t i l i z a t i o n o f Th232 i n t h e core r e g i o n o f p r e s e n t o x i d e - f u e l e d FBRs i s t o t a l l y i m p r a c t i c a b l e . Th232 i n t h e core r e g i o n i s t h u s a d d r e s s e d o n l y m a r g i n a l l y .
The f o l l o w i n g p r o b l e m s a r e a s s o c i a t e d w i t h t h e u s e o f Th232 i n t h e core r e g i o n :
--
The b r e e d i n g r a t i o i s r e d u c e d s i g n i f i c a n t l y o n a c c o u n t o f t h e d r a s t i c a l l y d e c r e a s e d f a s t - f i s s i o n c o n t r i b u t i o n .--
U233 b r e d i n t h e core h a s a s m a l l e r T-I: t h a n Pu239 ( s e e T a b l e I I . 1 9 ) , w h i c h h a s a n a d d i t i o n a l , n e g a t i v e i n f l u e n c e o n B% (see d i s c u s s i o n i n S e c t i o n 1 1 . 9 . a ) .--
The h i g h power d e n s i t y i n t h e core r e g i o n c a u s e s a h i g h e q u i l i b r i u m c o n c e n t r a t i o n o f P a 2 3 3 , l e a d i n g t o c o n -s i d e r a b l e s h u t d o w n c o n t r o l p r o b l e m s a f t e r r e a c t o r s h u t - down.
--
The h i g h b u i l d u p o f U232 i n t h e c o r e z o n e s ( h i g h n e u t r o n f l u x ) l e a d s t o a d d i t i o n a l p r o b l e m s i n f u e l r e f a b r i c a t i o n .--
T h e r e i s a m i x t u r e o f U233 a n d Pu239 a s f i s s i l e f u e l i n t h e core i f Th232/Pu239 i s t h e i n i t i a l f u e l ; t h i s i m - p l i e s m i x e d r e p r o c e s s i n g o f b o t h t h e t h o r i u m a n d ' u r a - nium c y c l e s .--
The f i s s i l e i n v e n t o r y i n c r e a s e s i f t h e power d e n s i t y r e m a i n s u n c h a n g e d .The o n l y a t t r a c t i v e a s p e c t o f u s i n g t h o r i u m i n t h e core r e g i o n i s l i m i t e d t o t h e d i s t i n c t l y l o w e r s o d i u m v o i d c o e f f i c i e n t . I n t h e case o f a ~ 2 3 8 / ~ u - f u e l e d " FBR, t h e s o d i u m v o i d becomes p o s i t i v e d u e t o s p e c t r u m h a r d e n i n g d u r i n g s o d i u m v o i d i n g , w h i c h c a u s e s a n
i n c r e a s e i n t h e f a s t f i s s i o n o f U238 a n d Pu240, and a h i g h e r neu-
c e r t a i n l y d e c r e a s e t h e i r b r e e d i n g r a t i o s t o b e l o w 1 . 0 , making
The r a d i a l b r e e d i n g g a i n G i n t h e c a s e o f t h e Tho2 b l a n k e t r
was found t o b e a p p r o x i m a t e l y 2 % above t h e Gr o f a U 0 2 b l a n k e t , and t h a t o f t h e ~ h ~ b l a n k e t a p p r o x i m a t e l y 1 2 % h i g h e r t h a n t h a t o f a U 0 2 b l a n k e t .
The g l o b a l b r e e d i n g r a t i o B s o f t h e FBR was, i n t h e c a s e o f t h e Tho2 b l a n k e t , r e d u c e d by 1 % a s compared t o a U 0 2 b l a n k e t , and no n o t i c e a b l e d i f f e r e n c e was o b s e r v e d f o r t h e ~ h ~ b l a n k e t . The g l o b a l b r e e d i n g g a i n GN o f t h e FBH w a s a p p r o x i m a t e l y 3%
l o w e r i n t h e case o f t h e Tho2 b l a n k e t and 0 . 5 % l o w e r f o r t h e
~ h ~ b l a n k e t t h a n f o r a U 0 2 b l a n k e t .
The s u p e r i o r b r e e d i n g p r o p e r t i e s o f t h e two t h o r i u m b l a n k e t s w e r e h i g h l i g h t e d by t h e ~ h ~ b l a n k e t . I t s s u p e r i o r i t y c a n b e
a s c r i b e d t o t h e n e u t r o n s p e c t r u m , w h i c h i s h a r d e r i n a m e t a l l i c t h a n i n a n o x i d e r a d i a l b l a n k e t . A s m a l l i n c r e a s e i n t h e f i s s i l e i n v e n t o r y i s r e q u i r e d w i t h Th b l a n k e t s , w h i c h was 1 . 2 % f o r t h e Thol b l a n k e t and 2.37% f o r t h e ~ h ~ b l a n k e t above t h e f i s s i l e i n - v e n t o r y o f a U 0 2 b l a n k e t .
The b u i l d u p o f Pa233 i s m o d e r a t e i n r a d i a l Th b l a n k e t s , c a u s i n g n o p a r t i c u l a r c o n t r o l p r o b l e m s .
The b u i l d u p o f U232 was k e p t b e l o w 300 ppm f o r a r e s i d e n c e t i m e l e s s t h a n 5 c y c l e s ( 1 c y c l e = 292 d a y s ) . T h i s c o n c e n t r a - t i o n l e v e l i s below t h e e x p e c t e d d e s i g n v a l u e o f HTR r e f a b r i c a - t i o n p l a n t s ( t h o r i u m c y c l e ) .
The sodium v o i d c o e f f i c i e n t was a p p r o x i m a t e l y 1 0 % l a r g e r f o r t h e Th b l a n k e t s t h a n f o r t h e U 0 2 b l a n k e t . T h i s i s , however, w i t h - i n t h e r a n g e o f u n c e r t a i n t y o f sodium v o i d c o e f f i c i e n t c a l c u l a t i o n s .
T h e r e i s n o p a r t i c u l a r i n c e n t i v e t o r e c y c l e t h e r a d i a l b l a n - k e t - b r e d U233 i n t o t h e c o r e r e g i o n o f t h e FBR s i n c e U233 i s a s l i g h t l y l e s s f a v o r a b l e f i s s i l e f u e l i n t h e FBR c o r e r e g i o n t h a n Pu239/Pu241.
CHAPTER 111. ASSESSMENT OF THE NEUTRON AND FISSILE FUEL UTILIZATION OF THE HTR
111.1. INTRODUCTION
The HTR is a thermal reactor that requires for its operation a continuous supply of fissile fuel. The fissile isotope usu- ally employed is U235, because the other fissile isotopes U233 and Pu239 are either not available in sufficient quantity or un- desirable as fissile fuel. The uranium ore (U 0 ) demand asso-
3 8
ciated with the U235 requirement makes the HTRs of present de- sign dependent on the continuous availability of uranium ore.
One of the most important parameters with respect to HTR fuel utilization is the actually necessary amount of uranium ore, or the fissile fuel U235 needed to sustain reactor operation.
This quantity is usually directly proportional to (1-CR), with CR being defined as the HTR conversion ratio, which is normally less than 1.0. Thus little additional fissile fuel, or makeup fuel, is necessary for an HTR with a large conversion ratio of approximately 0.8 to 0.9, but considerably larger amounts in the case of a relatively small CR
- -
0.5-
0.6.The HTR conversion ratio CR is primarily determined by the fuel cycle employed, and to some extent by the operational mode and design of the reactor. Disregarding the latter two dependen- cies temporarily, one can show that CR is largely a function of the combinations of fertile and fissile isotopes used, with U238 and Th232 as fertile, and U233, U235, and Pu239 as fissile iso- topes.
The results of Chapter I1 have shown that the breeding of U233 in the radial blanket region of the FBR is a feasible alter- native to Pu239 breeding, if there is a proper incentive to do so. It has been mentioned, however, that there is no particular advantage in recycling this U233 into the FBR core region.
T h e r e f o r e , t h e q u e s t i o n a r i s e s a s t o w h e t h e r t r a n s f e r o f t h e
T a b l e 1 1 1 . 1 . F i s s i l e a n d f e r t i l e i s o t o p e s o f v a r i o u s t h o r i u m
T h i s o n e - g r o u p method i s a t t r a c t i v e f o r i t s u n i v e r s a l i t y , t r a n s p a r e n c y , a n d c o m p r e h e n s i v e n e s s : it i s a p p l i c a b l e t o t h e HTR f u e l c y c l e s c o n s i d e r e d h e r e , a n d i t makes c l e a r t h e r e l a t i o n s h i p s b e t w e e n t h e n u c l e a r p a r a m e t e r s and t h e d e s i g n p a r a m e t e r s p e r t i n e n t t o t h e f i s s i l e f u e l economy o f t h e HTR; a n d , m o s t i m p o r t a n t , i t a l l o w s a c o m p r e h e n s i v e o v e r v i e w o f t h e HTR p o t e n t i a l i n terms o f f u e l u t i l i z a t i o n a n d d e s i g n c h a r a c t e r i s t i c s .
F o r e x a m p l e , r e l i a b l e e s t i m a t e s o f t h e i m p a c t o f d e s i g n c h a n g e s on t h e c o n v e r s i o n r a t i o , s u c h a s r e d u c e d n e u t r o n Leakage o f d e c r e a s e d f i s s i o n p r o d u e t p o i s o n i n g , c a n b e e a s i l y o b t a i n e d , w i t h o u t e x t e n s i v e b u r n u p c a l c u l a t i o n s .
The a c c u r a c y o f t h i s o n e - g r o u p model i s v e r i f i e d w i t h t h e r e s u l t s o f b u r n u p c a l c u l a t i o n s p e r f o r m e d a t t h e n u c l e a r r e s e a r c h c e n t e r K e r n f o r s c h u n g s a n l a g e (KFA) J i i l i c h , F. R . G .
S e c t i o n 1 1 1 . 3 g i v e s a n o u t l i n e o f t h e m e t h o d o l o g y ; a more e x t e n s i v e d i s c u s s i o n i s c o n t a i n e d i n A p p e n d i x 1 I I . A . The
r e l e v a n t g l o b a l n e u t r o n p a r a m e t e r s a r e e v a l u a t e d and d i s c u s s e d i n S e c t i o n 1 1 1 . 4 , and S e c t i o n 1 1 1 . 5 s u m m a r i z e s t h e r e s u l t s o f t h e f i s s i l e f u e l c y c l e a s s e s s m e n t s p e r f o r m e d a n d d i s c u s s e d i n d e t a i l i n Appendix 1 I I . B .
1 1 1 . 2 . DESCRIPTION OF THE FISSILE AND FERTILE FUEL
FLOWS I N THE VARIOUS FISSILE FUEL CYCLES
The i n h e r e n t d e s i g n f l e x i b i l i t y o f t h e HTR o f f e r s t h e p o s s i - b i l i t y o f u s i n g e i t h e r t h e t h o r i u m c y c l e ( f e r t i l e i s o t o p e Th232) o r t h e u r a n i u m c y c l e ( f e r t i l e i s o t o p e U 2 3 8 ) . Each f u e l c y c l e r e q u i r e s a f e e d o f f i s s i l e f u e l a s makeup, however.
S i n c e t h e makeup c o u l d b e U233, U235, o r Pu239, t h e r e a r e t h r e e c o n c e i v a b l e f i s s i l e f u e l c y c l e s t o e a c h f u e l c y c l e . They c a n b e r e d u c e d t o two f i s s i l e f u e l c y c l e s p e r f u e l c y c l e s i n c e t h e r e i s n o p a r t i c u l a r i n c e n t i v e t o s u p p l y t h e t h o r i u m c y c l e , c o n v e r t i n g
Th232 t o U233, w i t h Pu239 a s f i s s i l e f u e l . The o n l y L o g i c a l makeup f i s s i l e i s o t o p e s f o r t h e t h o r i u m c y c l e a r e e i t h e r U235 o r U233. A s i m i l a r l i n e o f r e a s o n i n g a p p l i e s t o t h e u r a n i u m c y - c l e , f o r w h i c h U233 a s makeup f u e l i s i m p r a c t i c a l .
The number o f f i s s i l e f u e l c y c l e s p e r f u e l c y c l e i n c r e a s e s
f u t u r e , t h e r e w o u l d b e a c h o i c e o f o p e r a t i n g t h e HTR o n a n y o n e o f t h e f o u r f i s s i l e f u e l c y c l e s , A , B , E l o r F , p r o v i d e d t h e a p p r o p r i a t e f i s s i l e f u e l makeup i s a v a i l a b l e . F o r t h e f o l l o w i n g d i s c u s s i o n o f t h e s e f o u r f i s s i l e f u e l c y c l e s , i t w i l l t a c i t l y b e a s s u m e d t h a t s u c h r e p r o c e s s i n g f a c i l i t i e s e x i s t .
1 1 1 . 3 . BASIC EQUATIONS RELATING TO THE F I S S I L E FUEL ECONOMIES OF THE VARIOUS F I S S I L E FUEL CYCLES
Some o f t h e b a s i c e q u a t i o n s n e c e s s a r y f o r e v a l u a t i n g t h e f i s s i l e f u e l e c o n o m i e s o f t h e v a r i o u s f i s s i l e f u e l c y c l e s a r e b r i e f l y i n t r o d u c e d h e r e . A d d i t i o n a l d i s c u s s i o n s a r e f o u n d i n A p p e n d i c e s 1 I I . A a n d 1 I I . B .
1 1 1 3 . a . F i s s i l e F u e l Demands d Z a n d d Z
us
The n e t f i s s i l e fue 2 demand d Z , i n kg/GW ( t h l d , i s g i v e n by E q u a t i o n ( I - 3 6 ) , s u c h t h a t
( 1 + a ) I z i s w e i g h t e d o v e r t h e c o m p o s i t i o n o f a l l f i s s i l e i s o t o p e s i n t h e c o r e . T h i s v a l u e h e a v i l y d e p e n d s o n t h e p a r t i c u l a r f i s s i l e f u e l c y c l e s i n c e e a c h h a s a d i f f e r e n t f i s s i l e i s o t o p e c o m p o s i t i o n .
I n t h e n o n r e c y c l i n g f i s s i l e f u e l c y c l e s C a n d D l d Z r e p r e - s e n t s t h e d i f f e r e n c e b e t w e e n t h e U235 l o a d e d , d e f i n e d a s d ,
us ,
a n d t h e s e l f - b r e d f i s s i l e f u e l s d i s c h a r g e d , Pu239 o r U233, d e f i n e d a s a a n d g i v e n i n E q u a t i o n ( 1 1 1 - 4 ) ' .
z
E q u a t i o n ( 1 1 1 - 1 ) d o e s n o t y i e l d t h e a c t u a l U235 demand t o b e s u p p l i e d a s makeup. I t c a n b e shown t h a t d:', t h e U235 m a k e u p ,
i n kg/GW ( t h l d , i s g i v e n b y
u s .
( 1 + a ) U5 i s t h e f i s s i l e f u e l c y c l e - w e i g h t e d ( 1 + u ) ,
US I Z
( F m / F I z i s t h e f i s s i o n f r a c t i o n o f t h e U235 makeup ( s e e
Appendix 111. A )
,
a n dw : ~
a s s u m e s t h e m e a n i n g d e f i n e d i n E q u a t i o n ( 1 - 3 2 ) ; W H 1 v a l u e s f o r t h e v a r i o u s f i s s i l e i s o t o p e s i a r e g i v e n b e l o w 3.
A s i s shown i n some g r e a t e r d e t a i l i n Appendix I I I . A . l , t h e f i s s i o n f r a c t i o n o f t h e U235 makeup c a n b e g i v e n by
w h e r e (FE5/F I ) i s t h e f i s s i o n f r a c t i o n o f t h e s e l f - g e n e r a t e d U235, i . e . U235 p r o d u c e d b y s u c c e s s i v e n e u t r o n c a p t u r e i n U233 a n d U234. T h e s e f i s s i o n f r a c t i o n s o f U235 m u s t b e d e t e r m i n e d b e f o r e t h e d e s i r e d U235 f e e d d y 5 , E q u a t i o n (111-2)
,
c a n b e e v a l - u a t e d . T h i s i n p a r t i c u l a r h o l d s f o r f i s s i l e f u e l c y c l e s B , C , D , a n d E .I f d Z a n d d Z u5
,
i n k g / G W ( t h ) d , a r e known, t h e n a Z , t h e amount o f s e l f - b r e d f i s s i l e f u e l d i s c h a r g e d (U233 o r P u 2 3 9 ) , c a n b ee v a l u a t e d f o r t h e n o n r e c y c l e f i s s i l e f u e l c y c l e s C a n d D by
'I£ t h e u s a b l e e n e r g y r e l e a s e d p e r f i s s i o n i s assumed t o b e 200 M e V , t h e n :
w i t h
w i t h d:5 a n d d Z g i v e n b y E q u a t i o n s ( 1 1 1 - 2 ) a n d 1 1 1 - )
,
r e s p e c - t i v e l y . H o w e v e r , t h e s e t w o e q u a t i o n s c a n o n l y be d e t e r m i n e d i f t h e f i s s i o n f r a c t i o n d i s t r i b u t i o n ( F ~ / F I ) i s known. I t c a n b e f o u n d i f t h e c o n v e r s i o n r a t i o CRZ f o r f i s s i l e f u e l c y c l e z i s known.I I I . 3 . b . C o n v e r s i o n R a t i o C R Z
Common t o a l l f i s s i l e f u e l c y c l e s i s t h e r e l a t i o n o f t h e c o n v e r s i o n r a t i o , w h i c h i s g i v e n b y E q u a t i o n ( 1 - 2 5 ) a n d d e r i v e d i n A p p e n d i x I . C . 1 :
CRZ i s s e e n t o be d e t e r m i n e d b y t w o g l o b a l n u c l e a r p a r a m e t e r s t h a t w i l l b e shown t o b e l a r g e l y i n d e p e n d e n t o f e a c h o t h e r : t h e f r a c t i o n a l p a r a s i t i c n e u t r o n l o s s e s P , d e f i n e d i n E q u a t i o n
( 1 - 5 1 , w i l l b e shown t o b e p r i m a r i l y d e t e r m i n e d b y r e a c t o r
-F I
d e s i g n a n d f u e l b u r n u p ; a n d q , , t h e number o f n e u t r o n s r e l e a s e d p e r f i s s i l e a b s o r p t i o n a n d a v e r a g e d o v e r t h e f i s s i l e i s o t o p e s , w i l l b e f o u n d t o d e p e n d o n t h e r e s p e c t i v e f i s s i l e f u e l c y c l e .
I f t h e f a c t o r s a n d r e l a t i o n s h i p s d e t e r m i n i n g t h e s e t w o p a r a m e t e r s a r e known, i t i s p o s s i b l e t o make a f u n d a m e n t a l a s s e s s m e n t o f - HTR f u e l u t i l i z a t i o n .
q z i s g i v e n b y t h e f o l l o w i n g s e t o f E q u a t i o n s ( I - 2 6 ) , ( I - 2 7 ) , a n d ( I - 2 8 ) , d e r i v e d i n A p p e n d i x I . C . l :
( F i / ~ I
I z
i s t h e f i s s i l e f u e l c y c l e - d e p e n d e n t f i s s i o n f r a c t i o n o fI I I . 4 . a . P a r a s i t i c N e u t r o n L o s s e s P i n t h e HTR
A s i s t h e c a s e i n t h e FBR, a c o n s i d e r a b l e f r a c t i o n o f t h e n e u t r o n s a v a i l a b l e i s l o s t i n t h e HTR by p a r a s i t i c a b s o r p t i o n a n d l e a k a g e . T h e s e p a r a s i t i c l o s s e s a r e g i v e n i n E q u a t i o n ( 1 - 5 ) a s
w h e r e t h e r i g h t hand t e r m s r e p r e s e n t t h e f r a c t i o n a l n e u t r o n l o s s e s : L i s d u e t o l e a k a g e , FP i s l o s s e s d u e t o a b s o r p t i o n i n f i s s i o n p r o d u c t s , S t i n s t r u c t u r a l m a t e r i a l , M i n t h e m o d e r a t o r , . C i n t h e c o n t r o l r o d s , a n d R i n p a r a s i t i c a c t i n i d e s 4
.
T a b l e 1 1 1 . 2 l i s t s t h e c o n t r i b u t i o n s o f t h e s e t e r m s t o p a r a - s i t i c a b s o r p t i o n P f o r s e v e r a l HTR r e f e r e n c e d e s i g n s ; t h e y a r e e x t r a c t e d f r o m t h e n e u t r o n b a l a n c e s o f b u r n u p c a l c u l a t i o n s p e r - formed a t KFA ( T e u c h e r t e t a l . 1 9 7 2 , 1974a a n d b ; S c h u l t e n e t a l . 1 9 7 7 ) . The r e l e v a n t f u e l c y c l e s o f t h e HTR i n v e s t i g a t e d a r e g i v e n i n t h e s e q u e n c e o f t h e n o m e n c l a t u r e o f T a b l e 1 1 1 . 1 .
4~ c a n a l s o b e d e t e r m i n e d a s
w i t h
i s t h e p a r a s i t i c a b s o r p t i o n i n e a c h o f t h e i n t e r m e d i a t e a c t i n i d e s P a 2 3 3 , Np239, e t c ; A i + l i s t h e p a r a s i t i c a b s o r p t i o n i n a c t i n i d e s s u c h a s U236, Pu242, Np237. A b s o r p t i o n o f a n e u t r o n i n Pa233 o r Np239 means l o s s o f t h e n e u t r o n a n d t h e l o s s o f f i s s i l e i s o t o p e U233 o r Pu239, c o n s t i t u t i n g a d o u b l e e n t r y i n t h e n e u t r o n b a l a n c e .
C J
e . g . c a s e s A-1, A - 2 , e t c , r e p r e s e n t b u r n u p c a l c u l a t i o n s f o r f i s s i l e f u e l c y c l e A .
Table 111.2. Distribution of the parasitic loss fractions of the HTR for various fissile fuel cycles and designs (burnup and reactor size), taken from available burnup cal- culations. -- -- .- - Fissile Reactor Fuel Fission products P = I, + FP + (St + M) + R fuel power burnup - P Reference cycle1 GW(th) G~d/t Xe S F P I, St + M R 'I'l~orium cycle: .0134 -1227 Case 4022/~2 Teuchert 1974c* -0173 -1452 Case 14907 Teuchert 1974c* .0111 .I041 Case3212 Teuchert 1976 B- 1 1 113 .0216 .0988 .I204 .0893 .0325 .2422 Case B Teuchert 1974a 8-2 1 9 2 -0208 .0849 .I057 .0747 .0157 .0279 .2246 CaseXI Teuchert 1974a C- 1 2.7 106 -0217 -0995 .I212 .0673 .0177 .0228 -2290 Ref.Case 1 Teuchert1974b C- 2 1 110 ,0221 .I036 -1257 .0930 .0369 .2556 Case 48200 1,ohnert 1973** C- 3 1 11 1 -0219 .lo3 -1248 .0906 .0379 .2524 Case A Teuchert 1974a C- 4 1 9 1 .0215 -0916 -1131 .076J .0175 .0224 .2240 Ref. Case I Teuchert 1974a C- 5 3 2 3 .021 .0495 .0705 .0484 .0326 -1515 Case 323-B Teuchert 1976* Uranium cycle: - -- -- -- (St -k M)
+
R, FP Xe. 1For fissile fuel cycle designations see Table 11.1..0084 -1867 Case 23502 Lohnert 1974** .0109 ,2314 Case 18200 Lohnert 1973** .009 -1830 LOTTO I11 Teuchert 1974a Case IV Teuchert 1972 Case V Teuchert 1972 Case I Teuchert 1972 Case VI Teuchert 1972 -- ---- "Personal communication, KFA Jfllj.ch, F.R.G. *:tPersonal conm~unication, Gesellschaft fur Hnch- ternperatur, Aensberq, F.R.G.
A l s o i n d i c a t e d i n c o l u m n 2 i s t h e r e s p e c t i v e r e a c t o r p o w e r , re- f l e c t i n g t h e s i z e o f t h e core a n d h e n c e t h e l e a k a g e t e r m L . The f u e l b u r n u p i s t a b u l a t e d i n c o l u m n 3 . FP, t h e a b s o r p t i o n l o s s e s i n t h e f i s s i o n p r o d u c t s , i s s e p a r a t e d i n t o a x e n o n f r a c t i o n X e a n d a r e m a i n i n g S f r a c t i o n :
E x a m i n i n g t h e d i s t r i b u t i o n o f t h e p a r a s i t i c l o s s e s more c l o s e l y r e v e a l s t h a t
--
The l a r g e s t f r a c t i o n o f p a r a s i t i c l o s s e s i s d u e ' t o ab- s o r p t i o n s i n t h e f i s s i o n p r o d u c t s .--
The s e c o n d l a r g e s t l o s s e s o c c u r a s a r e s u l t o f l e a k a g e .--
The p a r a s i t i c l o s s e s i n t h e s t r u c t u r a l m a t e r i a l s a n d i n t h e m o d e r a t o r a r e i n s i g n i f i c a n t .--
The t o t a l p a r a s i t i c l o s s e s P r a n g e f r o m 0 . 1 8 t o 0 . 2 5 f o r b u r n u p s l a r g e r t h a n 8 0 G W d / t .--
The p a r a s i t i c x e n o n f r a c t i o n a p p e a r s t o r e a c h a n e q u i - l i b r i u m v a l u e o f X e = 0 . 0 2 f o r a l l b u r n u p s .--
The p a r a s i t i c l o s s e s i n t h e a c t i n i d e s a r e l a r g e r i n t h e t h o r i u m c y c l e t h a n i n t h e u r a n i u m c y c l e .T h e s e o b s e r v a t i o n s , w h i c h a r e now d i s c u s s e d i n m o r e d e t a i l , a r e i n some cases r e l a t e d t o t h e c o r r e s p o n d i n g v a l u e s o b s e r v e d i n
FBRs ( T a b l e 1 1 . 2 1 )
.
T h e m o s t i m p o r t a n t p a r a s i t i c l o s s e s i n t h e HTR a r e t h e
l o s s e s i n t h e f i s s i o n p r o d u c t s , F P , I n t h e t h e r m a l H T R s p e c t r u m , a c l e a r c o r r e l a t i o n s h o u l d b e o b s e r v a b l e b e t w e e n t h e S f r a c t i o n , w h i c h e x c l u d e s t h e X e l o s s e s , a n d f u e l b u r n u p . T h i s i s i l l u s - t r a t e d by F i g u r e 1 1 1 . 1 , i n w h i c h S i s p l o t t e d a s a f u n c t i o n o f f u e l b u r n u p . T h i s l o s s f r a c t i o n c l e a r l y i n c r e a s e s a s t h e b u r n u p s i n c r e a s e s ; f o r h i g h b u r n u p s , t h e u r a n i u m c y c l e w i t h
S 0 . 0 8 e x h i b i t s a s m a l l e r S f r a c t i o n t h a n t h e t h o r i u m c y c l e w i t h S
-
0 . 1 6 . 5 A t l o w b u r n u p s o f 20-30 GWd/t, S r e d u c e s t o6 ~ h e f i s s i o n p r o d u c t s o f U233 h a v e l a r g e r a b s o r p t i o n c r o s s s e c t i o n s , w h i c h e x p l a i n s t h e l a r g e r l o s s e s i n t h e t h o r i u m c y c l e .
Fuel Burnup ( GW(th)dlt
F i g u r e 1 1 1 . 1 . F r a c t i o n s o f n e u t r o n a b s o r p t i o n i n t h e f i s s i o n p r o d u c t s ( e x c l u d i n g X e a b s o r p t i o n s ) o f t h e HTR t h o r i u m a n d u r a n i u m c y c l e s , as a f u n c t i o n o f f u e l b u r n u p ( d a t a f r o m T a b l e 1 1 1 . 2 ) .
v a l u e s b e t w e e n 0 . 0 5 aild 0 . 0 4 . A d e c r e a s e i n f u e l b u r n u p t h u s l e a d s t o a s i g n i f i c a n t r e d u c t i o n o f S by a b o u t 0 . 0 5 t o 0 . 0 7 , o r 5 t o 7 p o i n t s . Comparing t h e s e v a l u e s w i t h t h e FP f r a c t i o n o f t h e FBR i n T a b l e 1 1 . 2 1 , o n e o b s e r v e s t h a t i n t h e FBR t h e f i s s i o n p r o d u c t l o s s e s a r e r e l a t i v e l y s i g n i f i c a n t f o r t h e t o t a l PN l o s s e s . The i m p a c t o f t h e b u r n u p on P a n d t h u s on C R o r B% i s t h e r e f o r e much l a r g e r i n t h e HTR t h a n i n t h e FBR.
The s e c o n d l a r g e s t p a r a s i t i c l o s s f r a c t i o n i n t h e HTR, l e a k - a g e l o s s e s L , i s s e e n t o v a r y b e t w e e n 0 . 0 4 a n d 0 . 1 0 . L l o s s e s a r e f o u n d t o b e l a r g e r w i t h HTR d e s i g n s o f power o u t p u t l e s s t h a n 1 G W ( t h ) , w h e r e a s a n i n c r e a s e i n p l a n t s i z e t o 3 ~ ~ ( t h ) d e c r e a s e s L t o 0 . 0 4 . The L r a n g e i n t h e FBR i s b e t w e e n 0 . 0 6 5 a n d 0 . 0 2 .
SNR 300, w i t h a p l a n t s i z e o f 0 . 3 G W ( e ) , c l e a r l y shows t h e l a r g e s t L o f 0 . 0 6 6 , w h e r e a s FBRs o f 1-2 G W ( e ) s i z e show L l o s s e s o f a b o u t 9 . 0 1 5 . T h e r e f o r e , l e a k a g e l o s s e s L a r e i n f l u e n c e d b y r e a c t o r s i z e i n b o t h FBRs a n d HTRs, w i t h FBRs e x h i b i t i n g a t e n d e n c y t o g e n e r a l l y l o w e r v a l u e s .
The l o s s e s i n t h e s t r u c t u r a l m a t e r i a l s , S t , a r e u n i m p o r t a n t
T a b l e 1 1 1 . 3 . E s t i m a t e d i n f l u e n c e o f f u e l b u r n u p a n d r e a c t o r s i z e on t h e n e u t r o n l o s s f r a c t i o n s FP ( f i s s i o n p r o d u c t s a n d x e n o n )
,
L ( l e a k a g e ),
R ( p a r a s i t i c a c t i n i d e s ),
a n d P ( t o t a l p a r a s i t i c n e u t r o n l o s s e s ) f o r t h e HTR t h o r i u m a n d u r a n i u m c y c l e s .
F u e l c y c l e Thorium c y c l e Uranium c y c l e
F i s s i l e f u e l c y c l e A t B, C D , E, F
L o s s f r a c t i o n s P L F P R P L F P R
R e a c t o r s i z e : 1 GW(th) - 2 4 . 0 9 . 1 2 . 0 3 . 2 3 .10 - 1 1 .O1 F u e l b u r n u p : 100 ~ ~ d / t
R e a c t o r s i z e : 3 GW(th)
F u e l burnup:--100 GWd/t .20 . 0 5 .12 . 0 3 . 1 9 . 0 6 . l l .01 -53 GWd/t . 1 5 . 0 5 . 0 8 . 0 2 .14 . 0 6 . 0 7 .O1 -30 GWd/t . 1 2 . 0 5 . 0 6 .O1 . l l . 0 6 . 0 5
-
-20 GWd/t . 1 0 . 0 5 . 0 4 .O1 . 0 9 . 0 6 - 0 3
-
P = L + F P + R + ( S t + M ) , F P = S + X e .
1 1 1 . 4 . b . HTR Spectrurp-Weighted ( 1
+
a ) a n d F i s s i l e I s o t o p e - D e p e n d e n t v1 V a l u e sThe n e u t r o n p a r a m e t e r s t h a t r e m a i n t o b e d e t e r m i n e d a r e t h e f i s s i l e i s o t o p e - a n d f i s s i l e f u e l c y c l e - d e p e n d e n t ( 1 + a ) Z v a l u e s i and t h e f i s s i l e i s o t o p e - d e p e n d e n t vi v a l u e s . The ( 1
+
a )&
v a l u e sh a v e t o b e e x t r a c t e d f r o m t h e b u r n u p c a l c u l a t i o n s , w h e r e a s t h e v i v a l u e s a r e shown t o b e i n d e p e n d e n t o f t h e f i s s i l e f u e l c y c l e . z
I n t h e HTR m o s t n e u t r o n s a r e a b s o r b e d i n t h e t h e r m a l o r e p i t h e r m a l n e u t r o n e n e r g y r a n g e . The d i s t r i b u t i o n b e t w e e n t h e t h e r m a l a n d e p i t h e r m a l a b s o r p t i o n s d e p e n d s on t h e p r e v a i l i n g neu- t r o n e n e r g y s p e c t r u m , w h i c h i n t u r n i s d e t e r m i n e d by t h e m o d e r a -
t i o n r a t i o . S i n c e d i f f e r e n t m o d e r a t i o n r a t i o s a r e e x p e c t e d f o r t h e v a r i o u s f i s s i l e f u e l c y c l e s , t h e v a l u e s o f t h e e n e r g y - d e - p e n d e n t g l o b a l n e u t r o n p a r a m e t e r s a r e a l s o e x p e c t e d t o d i f f e r f o r e a c h f i s s i l e f u e l c y c l e . The vi v a l u e s a r e e n e r g y d e p e n d e n t
T a b l e 1 1 1 . 4 . F i s s i l e i s o t o p e d a t a f o r t h e v a r i o u s f i s s i l e f u e l
m o d i f i e d GAM n u c l e a r d a t a s e t ( 3 0 t h e r m a l and 68 e p i t h e r m a l e n e r g y
Table 111.5. HTR spectrum-averaged (1
+
a ) i values* of fissile isotopes for various fissile fuel cycles and their -moderation ratios i?c/~HM from the burnup calcu- lations available.
Fissile Moderation
Fuel U233 U235 Pu239 Pu24 1 ratio
Cycle** N C / ~ H M
Thorium c y c l e
A- 1 1 .I26 A- 2 1 .I25 A- 3 1 .I23
Uranium c y c l e D- 1
D- 2 D-3 D- 4
*
Fissile fractions (Fi/F I and absorptions are extracted f rorn the neutron balances. (1 + a ) can be determined by using v i from Table 111.4 and the equation:* *
See Table 111.2. for references.* * *
Mean values for Pu239/241.Energy (eV 1
F i g u r e 1 1 1 . 2 . ( 1
+
a ) e n e r g y g r o u p d a t a f o r Pu239, U235, a n d U233 f r o m 0 t o 5 e V .h a v e a v e r y i m p o r t a n t i n f l u e n c e on t h e f i s s i l e f u e l c y c l e - s p e c i - f i c ( 1
+
a ) v a l u e s , s o t h a t a c o m p a r i s o n b e t w e e n t h e d a t a l i s t e d i n T a b l e s 1 1 1 . 4 a n d 1 1 1 . 5 a n d t h o s e p l o t t e d i n F i g u r e 1 1 1 . 2 i s n o t d i r e c t l y a p p l i c a b l e . However, t h e g e n e r a l t r e n d o f ( 1 + a ) ia s a f u n c t i o n o f n e u t r o n e n e r g y o r m o d e r a t i o n r a t i o i s c l e a r l y d e m o n s t r a t e d .
Some o f t h e d a t a i n F i g u r e 1 1 1 . 2 a r e t a k e n f r o m t h e d a t a s e t o f t h e HAMMER s y s t e m ( S u i c h and Honeck 1 9 6 7 ) , a n d some f r o m m e a s u r e - m e n t s p e r f o r m e d by Gwin e t a l . ( 1 9 7 6 ) . Gwin g i v e s t h e r a t i o s o f t h e a b s o r p t i o n a n d f i s s i o n c r o s s s e c t i o n s m e a s u r e d .
A s m a l l e r m o d e r a t i o n r a t i o Nc/NHM s h i f t s t h e n e u t r o n s p e c t r u m f r o m t h e t h e r m a l i n t o t h e e p i t h e r m a l e n e r g y r a n g e , w h e r e t h e ( 1 + a) v a l u e s f o r Pu239 and U235 a r e h i g h e r . U233, by c o n t r a s t , r e m a i n s
l a r g e l y c o n s t a n t o v e r t h e e n t i r e t h e r m a l a n d e p i t h e r m a l e n e r g y r a n g e s .
1- can be inferred from the energy dependence of the (1 + a)i values of U235 and U233 in Figure 111.2 that the moderation ratio
in the thorium cycle has relatively little influence on the HTR spectrum-averaged ( 1 + a) values, since i ( 1 + a)U3 is relatively
c LLat. The moderation ratio in the uranium cycle, on the other 7
iisnd, is considerably more significant due to the steep rise of ( 5
+
a ) of Pu239, iThe (1
+
a) values of the Pu isotopes, which were determined from the neutron balances available, still seem somewhat uncertain.4s regards thorium fissile fuel cycle C , however, Pu is only of minor significance; the Pu239 and Pu241 values, which seem quite
low, maybe fairly uncertain for all thorium fissile fuel cycles since they do not significantly influence fissile fuel utiliza- tion. By contrast, the U235 and U233 values determined for the thorium cycles must be highly reliable.
As regards fissile fuel cycles D , E, and F, i.e. the uranium cycle, burnup calculations were available only for cycle D.
he
(1 + a) values for the Pu isotopes (1 .460 and 1 .265 for ~ ~ 2 3 9 and Pu241, respectively) taken from these calculations probably require some revision. In the meantime, values of 1.59 and 1.41 have been published without accompanying neutron balances (Teuchert and Brandes 1975), which show closer agreement with the global
HTR data of (1
+
a ) = 1 .627 and ( 1+
a) pU41 = 1 -373 containedifi the ORIGEN code system (Bell 1973) and the data measured by Gwin et al. 1976 (Figure 111.2). For cases D to F , the values proposed in Teuchert and Brandes (1975) were accepted with the reservation that they might reauire revision. A comparison of
(1
+
a) l for the Pu isotopes in the D20 reactor (N. Pieroni, recalculations for Atucha, Argentina, personal communication, Gesellschaft fur Kernforschung, Karlsruhe, 1974) yields values of 1.526 for Pu239, 1.439 for Pu241, and 1.180 for U235. This is as far as the problem of accurary of such (1+
a)Z data can i be discussed here; a more detailed examination would exceed thescope of the present investigation.
1 1 1 . 5 . DESCRIPTION OF THE ONE-GROUP
T a b l e 1 1 1 . 6 . A c c u r a c y of t h e o n e - g r o u p model f o r f i s s i l e f u e l c y c l e p a r a m e t e r s i n c o m p a r i s o n t o e x a c t b u r n u p c a l c u l a t i o n s ( P v a l u e s t a k e n f r o m e x a c t c a l c u l a - t i o n s , ( 1
+
a ) 1 v a l u e s f r o m T a b l e 1 1 1 . 4 ) .A c c u r a c y
d i s c u s s e d s e p a r a t e l y . T a b l e s I I I . B . l t o I I I . B . 4 compare t h e
. -
method o n t h e b a s i s o f t h e r e s u l t s of t h e r e f e r e n c e b u r n u p
c a l c u l a t i o n s l i s t e d i n T a b l e 1 1 1 . 2 . The a c c u r a c y o f p r e d i c t i o n t h a t c a n b e o b t a i n e d f o r t h e r e l e v a n t f u e l u t i l i z a t i o n p a r a m e t e r s CRZ and d:' and f a r some o t h e r i m p o r t a n t p a r a m e t e r s i s summarized i n T a b l e 1 1 1 . 6 : CRZ c a n b e p r e d i c t e d u p t o 1 p o i n t ( 0 . 0 1 ) , and d:' up t o 3 % .
The a c c u r a c y o f t h e r e s u l t s l a r g e l y d e p e n d s o n t h e a v a i l - a b i l i t y o f r e l i a b l e ( 1 + a ) = and P v a l u e s . i The P v a l u e s w e r e shown t o b e w e l l p r e d i c t a b l e f o r a l l f i s s i l e f u e l c y c l e s , b u t t h e ( 1
+
a ) Z v a l u e s v a r i e d s i g n i f i c a n t l y among t h e i n d i v i d u a l i f i s s i i e f u e l c y c l e s . Based on t e n r e f e r e n c e b u r n u p c a l c u l a t i o n s , t h e ( 1+
a ) Z v a l u e s i n T a b l e i 1 1 1 . 4 f o r t h e t h o r i u m c y c l e c a n b e r e g a r d e d a s q u i t e r e l i a b l e . ( 1 + a ) i f o r t h e u r a n i u m c y c l e , onz
t h e o t h e r h a n d , s p e c i f i c a l l y f o r f i s s i l e f u e l c y c l e s E a n d F , a r e e s t i m a t e s , b a s e d on t h e b u r n u p c a l c u l a t i o n s f o r f i s s i l e f u e l c y c l e D. A r e l a t i v e l y s m a l l e r r o r ( - 5 % ) i n t h e s e v a l u e s w i l l a f f e c t t h e r e s u l t s q u i t e c o n s i d e r a b l y . I t i s f e l t , h o w e v e r , t h a t t h e ( 1