REACTOR STRATEGIES AND THE ENERGY CRISIS Wolf H a f e l e
W . S c h i k o r r November 19 7 3
Research R e p o r t s a r e p u b l i c a t i o n s r e p o r t i n g on t h e work o f t h e a u t h o r . Any views o r c o n c l u s i o n s a r e t h o s e o f t h e a u t h o r , and do n o t n e c e s s a r i l y r e f l e c t t h o s e o f IIASA.
R e a c t o r S t r a t e q i e s and t h e Enerqv C r i s i s * Wolf H a f e l e and W. S c h i k o r r * *
1. I n t r o d u c t i o n and H i s t o r i c a l Review
R e a c t o r s t r a t e g i e s a s a r e s e a r c h t o p i c came up i n t h e e a r l y s i x t i e s . A t t h a t t i m e l i g h t w a t e r r e a c t o r s (LWR), heavy w a t e r r e a c t o r s , advanced t h e r m a l r e a c t o r s , and b r e e d e r s were u n d e r development, and i t was n o t o b v i o u s what t h e i r r e l a t i v e r o l e i n s a t i s f y i n g a g i v e n demand o f e l e c t r i c i t y would b e . I n c e r t a i n q u a r t e r s , f o r i n s t a n c e , t h e r e was a s t r o n g f e e l i n g t h a t a n i n t e r m e d i a t e r e a c t o r g e n e r a t i o n would b e r e q u i r e d t o b r i d g e a gap t h a t was f e l t t o b e between t h e c a p a b i l i t i e s o f
l i g h t w a t e r r e a c t o r s and t h a t o f b r e e d e r r e a c t o r s . The heavy w a t e r r e a c t o r , t h e s p e c t r a l s h i f t r e a c t o r , and sometimes t h e h i g h t e m p e r a t u r e g a s c o o l e d r e a c t o r (HTGR) w e r e , among o t h e r s , c o n s i d e r e d t o be c a n d i d a t e s f o r s u c h an i n t e r m e d i a t e f u n c t i o n . Along w i t h i t went a r e f l e c t i o n on t h e d e s i r e d p a r a m e t e r s o f f a s t b r e e d e r r e a c t o r s (FBR). Along t h e s e l i n e s a t r a d i t i o n a l a t t i t u d e was p r e v a i l i n g by a s k i n g o n l y f o r s h o r t d o u b l i n g t i m e s of s u c h FBR's. The scheme o f a d o u b l i n g t i m e was
i n t r o d u c e d by t h e e a r l y p i o n e e r s a t Argonne N a t i o n a l L a b o r a t o r y and e l s e w h e r e . They were u n d e r t h e i m p r e s s i o n o f f a i r l y
*
T h i s p a p e r was p r e p a r e d f o r t h e IAEA S t u d y Group on R e a c t o r S t r a t e g y C a l c u l a t i o n s , Vienna, November 5-9, 1973, and a p p e a r e d i n t h o s e P r o c e e d i n g s .* *
I n s t i t u t f u r Angewandte S y s t e m t e c h n i k und R e a k t o r p h y s i k , Kernforschungszentrurn K a r l s r u h e .l i m i t e d uranium r e s o u r c e s . I n t h e e a r l y s i x t i e s i t was c l e a r , however, t h a t t h e uranium r e s o u r c e s would b e by no means s o l i m i t e d a s i t was o r i g i n a l l y assumed i n t h e l a t e f o r t i e s . N e v e r t h e l e s s , t h e c o n c e p t o f d o u b l i n g t i m e p r e v a i l e d . The d o u b l i n g t i m e i s t h e t i m e d u r i n g which a f a s t b r e e d e r r e a c t o r
(sometimes a f a s t b r e e d e r p o p u l a t i o n i s c o n s i d e r e d i n s t e a d ) h a s p r o d u c e d , by v i r t u e o f i t s b r e e d i n g q a i n , t h e amount o f
f i s s i o n a b l e m a t e r i a l t h a t e q u a l s i t s i n v e n t o r y of such
f i s s i o n a b l e m a t e r i a l . A s e c o n d b r e e d e r r e a c t o r t h u s can b e p u t i n t o o p e r a t i o n , and t h e o r i g i n a l b r e e d e r h a s d o u b l e ? . For t h e d o u b l i n g t i m e one f i n d s t h e f o l l o w i n g r e l a t i o n :
The d o u b l i n g t i m e h e r e r e f e r s o n l y t o t h e i n p i l e i n v e n t o r y o f one b r e e d e r r e a c t o r .
TD = d o u b l i n g t i m e i n d a y s
,
b = r a t i n g i n MWth/kg f i s s
,
o c o c = ( n , y ) c r o s s s e c t i o n a = -
of
'
of = f i s s i o n c r o s s s e c t i o n BR = b r e e d i n g r a t i o,
K = l o a d f a c t o r .
Only t h e p r o d u c t o f r a t i n g and b r e e d i n g r a t i o minus one c h a r a c t e r i z e s t h e d o u b l i n g t i m e . One m u s t , however, r e a l i z e t h a t t h e c o n c e p t o f d o u b l i n g t i m e r e f l e c t s on b r e e d e r s e l f m u l t i p l i c a t i o n . While t h i s i s s t i l l the p r e -
v a i l i n g c o n c e p t i n t h e USSR, t h e s i t u a t i o n i s d i f f e r e n t i f a g e n e r a t i o n of t h e r m a l r e a c t o r s i s used t o p r o v i d e t h e f i s s i o n a b l e m a t e r i a l f o r t h e f i r s t c o r e i n v e n t o r y o f f a s t b r e e d e r r e a c t o r s . I n s u c h a s i t u a t i o n t h e r o l e o f f a s t b r e e d e r b u i l d u p i s :
dP 1
3,-b , d t M c o r e
where
PB = i n s t a l l e d f a s t b r e e d e r c a p a c i t y
,
M c o r e = 1st c o r e i n v e n t o r y o f f i s s i o n a b l e m a t e r i a l
.
R e l a t i o n ( 2 ) i s v a l i d b e c a u s e i n l a r g e enough r e a c t o r s t h e f i r s t c o r e i n v e n t o r y i s d e t e r m i n e d b y t h e r e q u i r e d power o u t p u t o f a r e a c t o r and t h e t e c h n o l o g i c a l l y f e a s i b l e power r a t i n g :
M c o r e =
Q
i;
(Kg).
( 3 )Q i s t h e r e q u i r e d power o u t p u t i n MWth. I t i s t h e r e f o r e no l o n g e r t h e p r o d u c t o f b (BR
-
1 1 , b u t t h e r a t i n g b a l o n e t h a t g o v e r n s t h e r o l e o f b r e e d e r b u i l d u p .Along s u c h l i n e s , F.R. D i e t r i c h [l] s t u d i e d t h e i n t e r - p l a y o f t h e r m a l r e a c t o r s , advanced c o n v e r t e r s , and f a s t
b r e e d e r s . He c o n s i d e r e d , among o t h e r p a r a m e t e r s , i n p a r t i c u l a r t h e amount o f n a t u r a l uranium t h a t would b e r e q u i r e d u n t i l a p o p u l a t i o n of f a s t b r e e d e r s a l o n e c a n s a t i s f y t h e e l e c t r i c a l power demand. I f t h a t s i t u a t i o n h a s been r e a c h e d , t h e s u p p l y
o f n a t u r a l uranium a s t h e f u e l f o r s u c h a p o p u l a t i o n o f f a s t
b r e e d e r r e a c t o r s o n l y i s no l o n q e r a problem. For f a s t b r e e d e r s t h e u t i l i z a t i o n of a g i v e n amount o f n a t u r a l uranium i s b e t t e r
by a f a c t o r o f 50-80 i f compared w i t h a t h e r m a l r e a c t o r . F o r t h i s v e r y r e a s o n t h e f r a c t i o n o f t h e e l e c t r i c i t y g e n e r - a t i n g c o s t s t h a t goes i n t o t h e p r o v i s i o n o f uranium o r e i s e x t r e m e l y low, a b o u t 1°/oo. T h e r e f o r e , even e x t r e m e o r e p r i c e s c a n be a f f o r d e d . C o n s e q u e n t l y v a s t amounts o f low g r a d e uranium become a c c e s s i b l e , and t h e amount o f e n e r g y t h a t i s s o a v a i l a b l e i s t h e o r d e r o f 10 6 Q (1 Q z 1018 BTU o r 3.35 1 0 7 MW y e a r ) 12, 31.
S h o r t l y a f t e r D i e t r i c h ' s p a p e r , i t was t h e R e p o r t t o t h e P r e s i d e n t
[41
and i t s d i s c u s s i o n d u r i n g t h e T h i r d Geneva C o n f e r e n c e (1964) t h a t f u r t h e r i n t r o d u c e d t h e r e s e a r c h t o p i c o f r e a c t o r s t r a t e . & i e s . A t t h e same t i m e it was R. G i b r a t [51 who s t u d i e d t h e c o u p l i n g between t h e r m a l r e a c t o r s and f a s t b r e e d e r s by a t r a n s p a r e n t and s i m p l y a n a l y t i c a l model t h a t v e r y much h e l p e d t o u n d e r s t a n d t h e mechanisms i n v o l v e d . O t h e r a u t h o r s f o l l o w e d [6, 7 1 . A major s t u d y was p r e s e n t e d by t h e N u c l e a r Research C e n t e r o f K a r l s r u h e [8]. TheK a r l s r u h e i n v e s t i g a t i o n s came t o a p r e l i m i n a r y end i n a p a p e r by P . J a n s e n [9]. A comprehensive model f o r t h e s u p p l y o f e l e c t r i c a l e n e r g y by b o t h n u c l e a r and f o s s i l power p l a n t s was p r e s e n t e d by Harde and Memmert
[lo] .
A more comprehensiver e v i e w o f t h e work i n Germany i s g i v e n by H.F. Zech d u r i n g t h i s c o n f e r e n c e .
A s t h e r e s e a r c h on r e a c t o r s t r a t e g i e s e v o l v e d , i t became more and more o b v i o u s t h a t t h e c o n s i d e r a t i o n o f t h e consumption o f n a t u r a l uranium s e r v e d a s a h e u r i s t i c
p r i n c i p l e o n l y ; more and more c o n s i d e r a t i o n s o f t h e amount o f r e q u i r e d s e p a r a t i v e work, t h e t i m i n g f o r t h e r e l a t e d f u e l c y c l e s , a n d , above a l l , c o s t b e n e f i t r a t i o s [ll] come t o t h e f o r e f r o n t o f a t t e n t i o n .
I n t h e f o l l o w i n g a few s i g n i f i c a n t q u a l i t a t i v e r e s u l t s o f t h e i n v e s t i g a t i o n s on r e a c t o r s t r a t e q i e s t h a t w e r e made d u r i n g t h e s i x t i e s s h a l l be summarized:
a ) The e x p e c t e d consumption o f n a t u r a l uranium i n t h e w e s t e r n w o r l d f o r t h e p r o d u c t i o n o f e l e c t r i c a l power u n t i l t h e y e a r 2000 i s a few m i l l i o n t o n s ( - 4-6 m i l l i o n )
.
T h i s b a s i c a l l y assumes t h a t t h e m a j o r i t y o f t h e e l e c t r i c a l power p r o d u c t i o n i s t a k i n g p l a c e i n L W R ' s . I n t h a t c a s e t h e uranium consumption beyond t h e y e a r 2000 c o n t i n u e s t o grow h e a v i l y . b ) I f t h e L W R ' s a r e c o u p l e d t o FBR's u s i n g t h e o x i d e sa s f u e l (U02/Pu02)
,
t h e consumption o f n a t u r a luranium u n t i l 2000 h a s r e a c h e d v a l u e s o f 3-4 m i l l i o n t o n s and d e c r e a s e s o n l y s l o w l y . I f t h e c a r b i d e s a r e u s e d a s f u e l (UC/PuC) i n s t e a d , a b o u t 3 m i l l i o n t o n s w i l l b e consumed u n t i l 2000 and. t h e consumption d e c r e a s e s c o n s i d e r a b l y
C ) S e p a r a t i v e r e q u i r e m e n t s a r e s h a r p l y l i m i t e d o n l y i f t h e FBR u s i n g c a r b i d e s i s d e v e l o p e d and d e p l o i t e d .
S t a r t i n g d a t e s f o r s u c h deployment c o u l d b e between 1980 and 1985, and do n o t i n f l u e n c e t h e r e s u l t s v e r y much.
d ) A g e n e r a t i o n o f advanced t h e r m a l r e a c t o r s w i t h a h i g h Pu o u t p u t s u c h a s heavy w a t e r r e a c t o r s do n o t a p p e a r t o be a must. N e v e r t h e l e s s , t h e y would s p e e d up t h e i n t r o d u c t i o n of f a s t b r e e d e r s
i f t h e Pu r e q u i r e m e n t s f o r t h e f i r s t c o r e
i n v e n t o r y o f FBR's comes o u t t o be t h e l i m i t i n g f a c t o r .
e ) A s a f i g u r e o f o r i e n t a t i o n , i t i s r e a s o n a b l e t o assume t h a t by t h e y e a r 2000 r o u g h l y 50% o f t h e i n s t a l l e d c a p a c i t y c o u l d b e f a s t b r e e d e r s and a b o u t 90% o f t h e a n n u a l i n s t a l l a t i o n a t t h a t t i m e would be f a s t b r e e d e r s .
£1 B e n e f i t / C o s t r a t i o s , where t h e b e n e f i t r e l a t e s t o t h e p r i c e a d v a n t a g e of t h e FBR o v e r t h e LWR and t h e c o s t t o t h e R a D c o s t s o f t h e b r e e d e r , a r e low f o r t h e FBR t h a t u s e s t h e o x i d e s and c o m p a r a t i v e l y h i g h f o r t h e FBR t h a t u s e s t h e c a r b i d e s .
One s h o u l d r e c a l l t h a t t h e t a c i t a s s u m p t i o n s f o r t h e s e r e a c t o r s t r a t e g i e s o f t h e s i x t i e s were t h e f o l l o w i n g :
1) I t i s o n l y t h e g e n e r a t i o n o f e l e c t r i c a l power t h a t i s t o be t a k e n i n t o a c c o u n t .
2) Any g e n e r a t i o n of e l e c t r i c a l power i n n u c l e a r p l a n t s must b e j u s t i f i e d on s t r i c t l y e c o n o m i c a l grounds.
I f n u c l e a r power d o e s n o t meet t h a t c r i t e r i o n , i t i s f o s s i l power, e s p e c i a l l y o i l and g a s , t h a t i s t h e n i n t h e b u s i n e s s a u t o m a t i c a l l y .
3) I t i s t h e p r c c u r e m e n t o f Pu from t h e r m a l r e a c t o r s and i n p a r t i c u l a r t h e LWR's t h a t g o v e r n s t h e r o l e o f deployment of FBR1s.
4 ) One must e n v i s a g e a c o n t i n u e d economic a r o w t h . 2. Changes S i n c e t h e S i x t i e s : The Enerqy Problem
During t h e few y e a r s s i n c e t h e l a t e s i x t i e s , a number o f s o m e t i m e s - d r a s t i c developments have t a k e n p l a c e . The developments t h a t a r e o f m a j o r r e l e v a n c e h e r e a r e t h e f o l l o w i n g :
a ) I n t h e US, t h e e x p e c t e d LWR c a p a c i t y f o r 1980 i s a t -140 GWe. The f i g u r e s f o r Germany and J a p a n r e s p e c t i v e l y a r e -19 GWe and -25 GWe, and t h a t f o r t h e whole w o r l d -230 GWe (LWR)
.
b ) I n t h e US, Germany, and Japan, i . e . t h e c o u n t r i e s w i t h l a r g e LWR p o p u l a t i o n s , t h e development o f FBR
i s d e l a y e d . Commercially s i g n i f i c a n t deployment i s now e x p e c t e d o n l y f o r t h e n i n e t i e s , w h i l e F r a n c e and England s t i l l e x p e c t a s i g n i f i c a n t l y e a r l i e r d a t e . These two c o u n t r i e s have a d e l a y e d o r no i n t r o d u c t i o n o f LWR1s.
C ) Energy p r i c e s have r i s e n g e n e r a l l y , sometimes d r a s t i c a l l y . I n 1970 t h e p r i c e f o r c r u d e o i l was
$ l / b a r r e l , now it i s a t $ 8 / b a r r e l .
d) S h o r t a g e s i n t h e s u p p l y o f f o s s i l f u e l have t o be e n v i s a g e d . P a r t l y t h i s i s due t o p o l i t i c a l c i r c u m s t a n c e s and p a r t l y t o t h e p h y s i c a l
l i m i t e d n e s s o f s u c h f u e l s . The t i m e s c a l e f o r t h e s e two t y p e s o f s h o r t a g e s i s q u i t e d i f f e r e n t . e ) U n l i m i t e d economic growth i s no l o n g e r an
u n c h a l l e n g e d a s s u m p t i o n .
f) A p p l i c a t i o n s f o r n u c l e a r e n e r g y o t h e r t h a n t h e g e n e r a t i o n o f e l e c t r i c a l power a r e now more and more e n v i s a g e d .
I t t h e r e f o r e a p p e a r s n e c e s s a r y t o r e v i e w a n d , i f n e c e s s a r y , t o expand t h e work on r e a c t o r s t r a t e g i e s o f t h e
s i x t i e s . The g u i d e l i n e f o r d o i n g t h a t must b e t h e c o n s i d e r a t i o n o f t h e whole e n e r g y s u p p l y problem and n o t o n l y t h e f r a c t i o n of t h e n u c l e a r g e n e r a t e d e l e c t r i c i t y . F u r t h e r , b e s i d e s t h e c o m p e t i t i v i t y , i t i s now a l s o a v a i l a b i l i t y o f e n e r g y t h a t m a t t e r s . To t h a t end one h a s t o r e f l e c t on t h e a v a i l a b i l i t y o f f o s s i l f u e l . For t h e p u r p o s e o f t h i s p a p e r i t w i l l be s u f f i c i e n t t o c o n s i d e r t h e f o l l o w i n g f i g u r e s on l i k e l y f o s s i l f u e l r e s e r v e s [12]:
c o a l o i l g a s o t h e r s t o t a l
The p r e s e n t and e x p e c t e d consumption o f t h e US and t h e w o r l d p r o v i d e s a y a r d s t i c k f o r j u d g i n g on t h e s e f i g u r e s .
us
w o r l d
T h i s s u g g e s t s we c o n s i d e r t h e problem o f t h e s u p p l y o f e n e r g y i n t h r e e p h a s e s [13]. The n e a r r a n g e p h a s e i s c h a r a c t e r i z e d by t h e f a c t t h a t any new t e c h n o l o g i c a l s t e p r e q u i r e s a b o u t 1 5 y e a r s b e f o r e i t can b e f e l t i n t h e
commercial domain. One s u c h new t e c h n o l o g y c o u l d b e l a r g e s c a l e s y n t h e t i c hydrocarbon p r o d u c t i o n a s a s u b s t i t u t e f o r o i l , making u s e o f n u c l e a r e n e r g y a s a s o u r c e f o r c h e m i c a l p r o c e s s h e a t o r n o t . T h i s c o u l d l e a d t o t h e renewed and e x t e n d e d u s e o f c o a l , a n d t h i s would t h e n c h a r a c t e r i z e a medium r a n g e p h a s e of t h e e n e r g y problem. A t h i r d p h a s e o f t h e e n e r g y problem comes i n t o p i c t u r e when f o s s i l f u e l becomes a s c a r c e m a t e r i a l , and n o n - f o s s i l f u e l h a s t o t a k e
o v e r a l l p h a s e s of p r o d u c t i o n , n o t o n l y t h e g e n e r a t i o n o f e l e c t r i c i t y . I t may be u s e f u l t o r e c a l l t h a t t h e p r e s e n t p a r t i t i o n between t h e p r i m a r y e n e r g y demand f o r e l e c t r i c i t y , t r a n s p o r t , h o u s e h o l d , commercial and i n d u s t r y i s , a s a r u l e o f thumb, 1:l:l:l. The f o l l o w i n g t a b l e summarizes t h e s e o b s e r v a t i o n s :
The Energy Problem
t i m e i n t e r v a l key word
n e a r r a n g e 1970-1985 ( ? ) o i l
medium r a n g e 1980-2000 ( ? ) c o a l / n u c l e a r l o n g r a n g e 1995- ( ? ) n o n - f o s s i l f u e l
There a p p e a r t o be f o u r o p t i o n s f o r t h e n o n - f o s s i l s u p p l y of a l l o f t h e e n e r g y : n u c l e a r f i s s i o n , n u c l e a r f u s i o n , s o l a r power, and g e o t h e r m a l e n e r g y i n t h e e a r t h ' s c r u s t [13:. I n t h e r e s t of t h i s p a p e r we w i l l c o n s i d e r o n l y t h e o p t i o n o f n u c l e a r f i s s i o n . N u c l e a r f i s s i o n can a l s o p r o v i d e n o n e l e c t r i c a l power [14]
.
I t i s i n p a r t i - c u l a r t h e HTGR t h a t h a s t h i s p o t e n t i a l . A s a s o u r c e o f c h e m i c a l p r o c e s s h e a t a t t e m p e r a t u r e s up t o 1 0 0 0 ~ C , i t c a n be u s e d t o s p l i t t h e w a t e r m o l e c u l e by s t a g e d c h e m i c a l p r o c e s s e s . Hydrogen h a s e x t r e m e l y a t t r a c t i v e f e a t u r e s a s a s e c o n d a r y f u e l [14]. I t i s t h e r e f o r e f e a s i b l e t o assume a s i t u a t i o n where, i n t h e l o n g r a n g e o f t h e e n e r g y problem, n u c l e a r f i s s i o n i s t h e s o u r c e o f p r i m a r y e n e r g y w i t h b o t h hydrogen and e l e c t r i c i t y a s s e c o n d a r y f u e l .3. New F u n c t i o n s o f Known R e a c t o r Types
The c o n s i d e r a t i o n s o f s e c t i o n 2 , i f t a k e n s e r i o u s l y , l e a d t o d r a s t i c c o n s e q u e n c e s . I n s o d o i n g o n e i s f i r s t l e d t o c o n s i d e r t h e l o n g r a n g e p h a s e a s t h i s e s t a b l i s h e s t h e l o n g r a n g e t a r g e t f o r a c o n s i s t e n t a p p r o a c h t o t h e e n e r g y p r o b l e m .
P . F o r t e s c u e [15] a n d work a t K a r l s r u h e h a v e p o i n t e d t o t h e p o s s l b l i t y o f u s i n g t h e b r e e d i n g g a i n o f FBR's, n o t
f o r t h e d o u b l i n g o f FBR's b u t , f o r t h e s u p p l y o f
u ~
To~ ~ .
t h a t e n d two v e r s i o n s o f an FBR seem f e a s i b l e . One v e r s i o n p r o v i d e s f o r p r o d u c t i o n o f
u~~~
i n t h e r a d i a l b l a n k e t o f a FBR. The Pu c y c l e o f s u c h a n FBR must b e , o f c o u r s e , s e l f - s u s t a i n e d . The b r e e d i n g r a t i o o f t h e c o r e and i t s a x i a l b l a n k e t m u s t t h e r e f o r e b e i n o p e r a t i o n a l terms e q u a l t o o n e . The o t h e r v e r s i o n i s t o u s e t h e i n n e r p o r t i o n o f t h e c o r e , r o u g h l y o n e h a l f o f t h e c o r e , f o r f u e l i n g w i t h P U / T ~ e l e m e n t s , a n d t o l e t t h e r a d i a l b l a n k e t b r e e d Pu. Work i s g o i n g on a t K a r l s r u h e t o examine b o t h v e r s i o n s in g r e a t e r d e t a i l [16].I t a p p e a r s t h a t i n s u c h a way enough
u~~~
c a n b e p r o v i d e d t o make up f o r t h e a n n u a l r e q u i r e m e n t o f a n HTGR which o p e r a t e s on t h e b a s i s o fu~~~
a n d Th. The r a t i owhere
PH = i n s t a l l e d HTGR c a p a c i t y i n GW, t h e r m a l
,
and PB = i n s t a l l e d FBR c a p a c i t y in GW, t h e r m a l,
c o u l d w e l l b e between 1 . 0 and 1 . 5 u n d e r c e r t a i n c o n d i t i o n s even h i g h e r t h a n t h a t .
I n s u c h a scheme t h e FBR d o e s n o t d o u b l e any more. The FBR s u s t a i n s t h e s t e a d y o p e r a t i o n o f an H T G ~ i n s t e a d . T h i s i m p l i e s a s t a t i c , non-expanding s i t u a t i o n where o n l y U 2 38 and T h - - i . e . a b u n d a n t n a t u r a l i s o t o p e s - - a r e consumed a s f u e l and b o t h t y p e s o f s e c o n d a r y f u e l a r e produced: e l e c t r i c i t y from t h e FBR and hydrogen from t h e HTGR. Such an approach r e a l l y employs t h e g e n u i n e a d v a n t a g e s of b o t h r e a c t o r t y p e s : t h e FBR b r e e d s Th i n t o
u ~
and t h e HTGR~ ~ ,
i s t h e r e f o r h i g h t e m p e r a t u r e s t h a t a r e a n e c e s s a r y c o n d i t i o n f o r s p l i t t i n gt h e w a t e r m o l e c u l e . To make e l e c t r i c i t y from t h e HTGR d o e s n o t g e n u i n e l y r e q u i r e h i g h t e m p e r a t u r e . I n f a c t , t h e HTGR i s d e g r a d e d t o be o n l y a c o m p e t i t o r f o r t h e LWR i n t h a t c a s e . And u n d e r t h e a s y m p t o t i c c o n d i t i o n o f a s o c i e t y w i t h n o growth, t h e d o u b l i n g of b r e e d e r s i s n o t d e s i r a b l e anyhow.
F i g u r e 1 c h a r a c t e r i z e s t h i s a s y m p t o t i c s o l u t i o n o f t h e l o n g r a n g e p h a s e o f t h e e n e r g y problem.
I f t h a t i s c o n s i d e r e d a t t r a c t i v e , t h r e e q u e s t i o n s come up:
-
What c o u l d b e an a p p r o a c h d u r i n g t h e medium r a n g e p h a s e of t h e e n e r g y problem?-
What i s t h e t i m i n g o f t h i s a p p r o a c h d u r i n g t h e medium r a n g e p h a s e ?-
What i s t h e n t h e i n t e r p l a y w i t h t h e f i n i t e r e s o u r c e s o f f o s s i l f u e l ?H e r e it i s proposed t o a p p r e c i a t e t h e s o l i d p o s i t i o n t h a t t h e LWR i s h a v i n g now and more s o i n t h e f u t u r e . The f a i r l y d r a s t i c a s s u m p t i o n i s b e i n g made t h a t f o r t h e n e x t o n e o r two d e c a d e s a l l i n c r e a s e d demands f o r e l e c t r i c power w i l l be m e t by LWR1s. LWR1s p r o d u c e r o u g h l y 170 Kg/GWe of p l u t o n i u m . The f u r t h e r d r a s t i c a s s u m p t i o n s h a l l h e made t h a t no Pu r e c y c l i n g i n LWR's s h a l l t a k e p l a c e . I n s t e a d , a l l Pu produced i n LWR1s s h a l l be used t o e s t a b l i s h t h e f i r s t c o r e i n v e n t o r i e s o f new FBR1s. I f P, d e n o t e s t h e i n s t a l l e d LWR
J J
d P ~ c a p a c i t y i n GWthemal, t h e n PL i n d u c e s i n t h i s way
-
d t.
More t h a n t h a t , t h e FBR f u n c t i o n s a s a w a s t e box f o r t h e d i s p o s a l o f t h e Pu produced i n t h e LWR. T h e r e t h e Pu does n o t i n c r e a s e f u r t h e r , b u t j u s t s t a y s t h e r e a s a permanent c a t a l y s t f o r t h e u s e o f
u~~~
and p a r t l y Th. The c o n d i t i o n s o f s u c h a t r a n s i e n t p h a s e c a n t h e r e f o r e b e summarized a s o u t l i n e d i n F i g u r e 2 . L e t u s r e c a l l :-
The FBR d o e s n o t d o u b l e any more. The r a t e o f i t s d P ~i n c r e a s e
dt
i s p r o p o r t i o n a l t o P L '-
The HTGR can be i n s t a l l e d p r o p o r t i o n a l l y t o t h e FBR, PH = BPB. I t produces, by v i r t u e of i t s h i g h t e m p e r a t u r e s , hydrogen.-
The i n c r e a s e of t h e whole e l e c t r i c i t y demand i s met i n t h e b e g i n n i n g o n l y by LWR1s.-
Pu t h a t i s produced i n t h e LWR1s g o e s i n t o t h e FBR.I t s t a y s t h e r e a n d d o e s n o t d o u b l e .
4 . A H i g h l y S t y l i z e d A n a l y t i c a l Model
The a p p r o a c h o u t l i n e d i n s e c t i o n 3 c a l l s f o r a model.
A t t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d Systems A n a l y s i s work i s g o i n g on t o e s t a b l i s h s u c h a computer model. A n e c e s s a r y f i r s t s t e p , however, i s t o h a v e a h i g h l y s t y l i z e d a n a l y t i c a l model t h a t a l l o w s f o r t h e u n d e r s t a n d i n g o f t h e mechanisms i n v o l v e d . I t s e r v e s a s a s k e t c h f o r t h e above m e n t i o n e d computer model.
Now w e s h a l l d e s c r i b e t h i s a n a l y t i c a l model. The demand f o r power, e i t h e r e l e c t r i c a l o r n o n e l e c t r i c a l , may b e des- c r i b e d b y a p o l y n o m i a l e x p r e s s i o n .
f o r 0 < t < t l .
Po d e n o t e s t h e v a l u e o f P ( t ) a t t = 0 , P = P1 a t t = t and 1
'
Ro i s t h e r e l a t i v e y e a r l y i n c r e a s e o f P a t t = t o . We assume t h a t a t t = t l , n o t o n l y P = P b u t a l s o ( - I t dP = 0 , o r i n
1 d t 1
o t h e r w o r d s , a no growth p a t t e r n a t t = t l . We t h e n f i n d
and
T i s o f a t r a n s i e n t n a t u r e t h a t a l l o w s f o r RO a t t = t o and S l e a d s i n t o t h e s t e a d y no growth s t a t e a t t = t l . F i g u r e 3 shows T and S a s f u n c t i o n s o f t i m e .
We now assume a model s o c i e t y G . A t t = t o G may have 250 1 0 p e o p l e w i t h 1 0 KW/capita t o t a l power demand. W i t h i n 6 40 y e a r s t h e p o p u l a t i o n s h a l l have l e v e l e d o f f a t 362 1 0 6 p e o p l e , i m p l y i n g an a v e r a g e growth r a t e f o r 0 < t < tl o f 0 . 9 2 % . For Ro we assume 4 . 5 % . Two s u b c a s e s a r e c o n s i d e r e d : i n one s u b c a s e t h e p e r c a p i t a demand f o r power h a s i n c r e a s e d t o 20 KW/capita, and i n t h e o t h e r s u b c a s e i t h a s remained c o n s t a n t a t 1 0 KW/capita. The n o t a t i o n f o r t h e t o t a l power demand may b e P t o t ( t )
.
The e l e c t r i c a l power demand, P e l ( t 1
,
s h a l l s t a r t a t t = 0 w i t h P e l ( 0 ) = 0.25 P t o t ( 0 ) and Ro = 8 % . One may r e c a l l : P e l i s t h e p r i m a r y e n e r g y demand t h a t g o e s i n t o t h e g e n e r a t i o n o f e l e c t r i c i t y , and i t i s measured i n GW, t h e r m a l . A t t = t l , we d e f i n e P e l ( t l ) = 0.'5 P t o t ( t l ).
I n o t h e r words, t h e r e l a t i v e s h a r e of e l e c t r i c i t y i n t h e t o t a l power p r o d u c t i o n s h a l l d o u b l e i n e i t h e r of t h e two s u b c a s e s c o n s i d e r e d .P p r i s t h e n o t a t i o n f o r t h e p r o c e s s h e a t , t h a t i s we have
P t o t = P e l
+
P p r.
(71F i g u r e 4 d e s c r i b e s t h e f i r s t s u b c a s e ( 2 0 KW/capita a t t = t l ) , w h i l e F i g u r e 5 d e s c r i b e s t h e s e c o n d s u b c a s e
( 1 0 KW/capita a t t = t l ) .
We now assume P ( 0 ) L = 0 , a t t = 0 t h e r e i s o n l y one f o s s i l power. F u r t h e r , we make t h e a s s u m p t i o n t h a t t h e
c a p a c i t y o f t h e n u c l e a r i n d u s t r y may f o l l o w t h e f u n c t i o n A l ( t )
.
T h i s i m p l i e swhere t d e n o t e s t h e t i m e when no more LWR's o r FBR's a r e E 11
b e i n g b u i l t . A s we w i l l see l a t e r , t > tl. For t h e E I 1
h i g h l y s t y l i z e d model p r e s e n t e d h e r e , we f u r t h e r assume A1 = c o n s t f o r 0 5 t 5 t E I l , and w i l l l a t e r v a r y t h e v a l u e o f A1. A1 r e f e r s t o t h e number o f LWR's and FBR's t h a t can b e b u i l t p e r y e a r . I t i s measured i n GWth p e r y e a r . W e s p e c i a l i z e f u r t h e r by assuming
6 P ~
-
-6 t
-
A1,
f o r 0-
< t ( t * .The a m o a t of Pu t h a t i s y e a r l y produced by one GW-LWR s h a l l be d e n o t e d by a L I p u , and c u m u l a t e amounts o f Pu by
.
A t t = t * we t h e n haveand
PE p r o d u c e s A
-
t * a of Pu p e r y e a r . T h i s i s s u f f i c i e n t L,Put o p r o v i d e t h e f i r s t c o r e i n v e n t o r i e s o f
6t
i f i~ ,Pu i s t h e f i r s t c o r e i n v e n t o r y ( i n c o r e
+ ;
i n c o r e f a r o u t o f p i l e p u r p o s e s ) f o r 1 GWe FBR. Here i n t h i s a n a l y t i c a l model we assume t h e same t h e r m a l e f f i c i e n c y f o r LWR's a n d FBR's. We f u r t h e r s p e c i a l i z e by assuming t h a tf o r t * ( t ( t E n l
.
E q u a t i o n s ( 1 2 ) and ( 1 3 ) imply t h a t
a ~ , ~ u = 170 Kg/GWe y e a r and i B l p u = 3.0 to/GWe, we h a v e t * = 17.6 y e a r s = 18 y e a r s
.
L e t u s assume t h a t 1970 i s t = 0 and t h e r e f o r e 1988 i s t * . Then t h e LWR c a p a c i t y o f 1988 i s s u f f i c i e n t t o f u e l a l l FBR's t h a t a r e b u i l t a t a y e a r l y r a t e o f A . I f t h e FBR comes e a r l i e r , more LWR's t h a n i n o p e r a t i o n a t t h a t e a r l i e r t i m e have t o be i n s t a l l e d i f t h e a n n u a l Pu o u t p u t a L l p u i s meant t o f u e l t h e s e b r e e d e r s . But t * = 18 y e a r s i s n o t an
u n r e a l i s t i c a s s u m p t i o n . We t h e r e f o r e do assume ( 1 3 ) h e r e i n t h i s a n a l y t i c a l s k e t c h .
T o g e t h e r w i t h t h e b r e e d e r s now, HTGR's c a n be b u i l t a n d o p e r a t e d f o r t h e i n c r e a s i n g p r o d u c t i o n o f n o n e l e c t r i c a l power.
Me assume t h a t t h e i r f i r s t c o r e i n v e n t o r y i s
u~~~
and t h a tt h e a n n u a l f u e l i n g i s
u~~~
which comes from t h e FBR's. W e t h e n have ( 4 ) :and we t h e r e f o r e assume
and
A2 = BA1
where t d e n o t e s t h e t i m e when no more HTGR's a r e b e i n g El2
b u i l t because t h e demand curve P p r i s m e t by H T G R ' s and no f o s s i l f u e l s a r e n e c e s s a r y any more.
Let t * * now be t h e t i m e when
p i *
+
P** B = P e l ( t * * ),
(17)o r i n o t h e r words, when a l l of t h e e l e c t r i c a l power r e q u i r e m e n t s a r e m e t by LWR's and FBR's. (Note: P** = P* because of (13) .)
1 1
For t h e p u r p o s e s of t h i s h i g h l y s t y l i z e d model we now f u r t h e r assume
T h i s l e a d s t o
Equation ( 1 8 ) i m p l i e s f o r t h e f i r s t subcase ( 2 0 KW/capita) A1
-
< 36/year and f o r t h e second subcase ( 1 0 KW/capita)A~ 1 8 / y e a r . Such r a t e s f o r t h e b u i l d i n g o f r e a c t o r s a r e r e a s o n a b l e f o r t h e model s o c i e t y G c o n s i d e r e d h e r e .
A t t = t * * we now c o n t i n u e t o b u i l d FBR's a t a r a t e o f A1. But t h e y a r e meant t o r e p l a c e L W R ' s and n o t t o f o l l o w demand i n c r e a s e s . Due t o t h e symmetry o f t h e model c o n s i d e r e d h e r e t h i s l e a d s t o
PL = 0 a t t =
t ~ , 1 and
We now r e c a l l t h a t we h a v e l e f t o v e r t h e Pu s t o c k p i l e f u e l t h a t was produced b e f o r e t * ( 0 < t < t * )
.
A f t e r t * * t h e LWR' s produce a g a i n t h e e q u i v a l e n t amount. We t h u s have a t t = t h e f o l l o w i n g amount o f Pu t h a t comes from t h e LWR d u r i n g t h e b u i l d u p and r e d u c t i o n p h a s e s :The amount of Pu t h a t i s r e q u i r e d t o c o n t i n u e w i t h t h e i n s t a l l a t i o n o f t h e FBR f o r t * *
5
t5
tE i sBoth amounts e q u a l , i f t * o b s e r v e s ( 1 4 ) . But t h i s was t h e d e f i n i t i o n o f t * . I n t h e c a s e c o n s i d e r e d h e r e , no P u ' i s
l e f t o v e r , t h u s t h e Pu b a l a n c e i s c l o s e d . A l l Pu e n d s up i n t h e FBR's.
I n t h e c a s e o f B = 1, t h a t i s PH = P B , t h e b u i l d u p o f H T G R ' s m e e t s t h e demand f o r n o n e l e c t r i c a l power, P p r , e x a c t l y a t t E l l . T h i s i s t h e c a s e b e c a u s e f o r t
2
t l , P p r = P e l , o r P e l = 0 . 5 P t o t .I n F i g u r e 6 we now i l l u s t r a t e t h e h i g h l y s t y l i z e d
and s y m m e t r i c a l c a s e c o n s i d e r e d h e r e which l e a d s t o c o m p l e t e l y c l o s e d m a t e r i a l b a l a n c e s .
Not s o h i g h l y s y m m e t r i c a l c a s e s a p p e a r i f
LWR's have t o b e b u i l t beyond t * i f t h e b r e e d e r comes t o o e a r l y . Such c o n t i n u e d LWR b u i l d u p f o l l o w s t h e f u n c t i o n
A s i m i l a r o b s e r v a t i o n i s t r u e beyond t * * when t h e L W R ' s a r e f i n a l l y r e p l a c e d by FBRvs. I n t h a t c o n n e c t i o n it must b e mentioned t h a t t h e v a r i o u s t i m e d e l a y s i n t h e n u c l e a r
f u e l c y c l e s have n o t been t a k e n i n t o a c c o u n t . F u r t h e r , B > 1 l e a d s t o s a v i n g s i n t h e
u~~~
f i r s t c o r e i n v e n t o r i e s o f t h e HTGR. V a l u e s of B t h a t a r e between one and two seem t e c h n i c a l l y f e a s i b l e [16].
T h i s l e a d s t o v a l u e s of t E l 2 c tE,l and a g a i n e x p l i c i t s t e p s h a v e t o b e t a k e n f o r t > t d u r i n g which t h e p r o d u c t i o n o fu~~~
i n b r e e d e r s wouldE,2
b e s l o w e d down. B = 1 i s t h e one s y m m e t r i c a l c a s e b e c a u s e we had assumed h e r e P p r ( t l ) / P e l ( t l ) = 1.
I f a d i f f e r e n t a s y m p t o t i c v a l u e of t h i s r a t i o i s e n v i s a g e d , B s h o u l d be a d j u s t e d a c c o r d i n g l y . We a l s o
P1
-
Poassumed A1 5
- .
I f a l a r g e r n u c l e a r c o n s t r u c t i o n c a p a c i t y i s c o n s i d e r e d , t h e n t h e c u r v e o f t h e e l e c t r i c a l demand i s met e a r l i e r a c c o r d i n g l y ; t h e c o n s t r u c t i o n o f new n u c l e a r power p l a n t s h a s t o f o l l o w t h a t demand c u r v e f o r a w h i l e . We a l s o assumed i m p l i c i t l y t h a t t h e t h e r m a l e f f i c i e n c y o f t h e FBR e q u a l s t h a t o f t h e LWR, which i s o b v i o u s l y an a p p r o x i m a t i o n . The l o g i c o f a l l t h e s e sub- c a s e s w i l l be t a k e n c a r e of i n o u r computer program. F o r t h e h e u r i s t i c p u r p o s e s of t h i s o u t l i n e , it i s s u f f i c i e n t t o c o n s i d e r t h e more s p e c i a l c a s e c o n s i d e r e d h e r e . The computer program w i l l a l s o t a k e c a r e of t h e v a r i o u s o p t i m i z a t i o n s i n v o l v e d . There a r e s t o c k p i l e s of P u , f o s s i l f u e l and n a t u r a l uranium,and i n v e s t m e n t s i n t h e LWR, i n t h e huge i s o t o p e s e p a r a t i o n p l a n t s and uranium m i n i n g . These i n v e s t m e n t s w i l l be o p e r a t i v e f o r a l i m i t e d p e r i o d o f t i m e o n l y . When t h e a s y m p t o t i c scheme of F i g u r e 1 becomes o p e r a t i v e , n o LWR's a r e i n o p e r a t i o n any more, n o e n r i c h - ment i s r e q u i r e d , and uranium mining f a l l s t o ad i f f e r e n t o r d e r o f magnitude. D e s p i t e t h e h i g h l y s t y l i z e d n a t u r e o f o u r a n a l y t i c a l model, we d i d make a n u m e r i c a l e v a l u a t i o n . A t t = t E , 1 ' n o f o s s i l f u e l i s r e q u i r e d any more. I t i s t h e r e f o r e m e a n i n g f u l t o e v a l u a t e t h e amount o f f o s s i l f u e l t h a t i s consumed w i t h i n 0
2
t5
t E l l . I t i s e q u a l l y i n t e r e s t i n g t o e v a l u e t h e amount o f n a t u r a lu r a n i u m t h a t h a s t o b e p r o v i d e d f o r w i t h i n t h a t t i m e
i n t e r v a l . To make q u i c k c o m p a r i s o n s , o n e f i n d s i t d e s i r a b l e t o e x p r e s s b o t h t h e amounts o f f o s s i l f u e l a n d t h e n a t u r a l u r a n i u m i n t e r m s o f Q . While t h i s i s s t r a i g h t f o r w a r d f o r t h e f o s s i l f u e l s , i t i s a d i f f i c u l t y i n t h e c a s e o f u r a n i u m . Roughly 20% o f t h e r e q u i r e d n a t u r a l u r a n i u m i s n e e d e d t o
p r o v i d e f o r t h e f i r s t c o r e i n v e n t o r i e s o f t h e LWR's a n d H T G R ' s . T h e s e f i r s t c o r e i n v e n t o r i e s h a v e n o t a f u e l b u t a c a t a l y t i c f u n c t i o n a s t h e c r i t i c a l mass h a s t o b e t h e r e b e f o r e t h e a n n u a l r e l o a d c a n b e b u r n e d . We t h e r e f o r e g i v e o n l y a n a r t i f i c i a l e q u i v a l e n t . A t y p i c a l LWR w i t h a g i v e n c r i t i c a l mass r e q u i r e s 2 . 5 1 0 t o 6 UNAT t o p r o d u c e 1 Q o f h e a t :
2 . 5 1 0 t o n a t u r a n i u m 6 = 1 Q (LWR e q u i v a l e n c e )
.
With t h e s e c l a r i f i c a t i o n s , o n e c a n now e x a m i n e T a b l e 1 a n d F i g u r e s 7 a n d 8 , a n d F i g u r e s 9 a n d 1 0 a s w e l l . F i g u r e s 7 a n d 8 r e f e r t o t h e s e p a r a t i v e work r e q u i r e m e n t s a s a f u n c t i o n o f t i m e f o r c a s e s 1 a n d 3 o f T a b l e 1, a n d
F i g u r e s 9 a n d 1 0 t o t h e demand f o r f o s s i l f u e l a c c o r d i n g l y . T a b l e 2 l i s t s t h e v a r i o u s n u m e r i c a l a s s u m p t i o n s t h a t w e r e made i n t h e c a l c u l a t i o n s .
While k e e p i n g i n mind t h a t t h e s e d a t a r e f e r t o a model, i t may b e s t i l l w o r t h w h i l e t o draw a number o f c o n c l u s i o n s .
1) Case 1 r e f e r s t o a n a s y m p t o t i c v a l u e o f 20 KW/cap f o r 3 6 2 10 6 p e o p l e a n d a n a n n u a l i n s t a l l a t i o n o f 36 n u c l e a r power s t a t i o n s , 1 GWe e a c h . Such a r a t e
i s r e a s o n a b l e . I t i s c l o s e t o f i g u r e s a n t i c - i p a t e d f o r t h e US L17]. Under t h e s e c o n d i t i o n s it t a k e s 58 y e a r s t o a r r i v e a t t h e FBR/HTGR a l F n u c l e a r e n e r g y s u p p l y scheme o f F i g u r e 1. To a r r i v e t h e r e r o u g h l y 4 Q ' s o f f o s s i l f u e l a r e r e q u i r e d . I f a narrow-minded e x t r a p o l a t i o n from 2 . 5 1 0 p e o p l e t o a world t o t a l o f 8
lo1'
p e o p l e i s a t t e m p t e d , t h i s would t h e n mean 160 Q . T h i s i s r o u g h l y t h e amount o f f o s s i l f u e l t h a t i s a t a l l a v a i l a b l e . A more r e a s o n a b l e approach t o t h e g l o b a l problem o f s u p p l y i n glo1'
p e o p l e w i t h s u f f i c i e n t amounts of e n e r g y would p r o v i d e f o r more d i s a g g r e g a t i o n . One c o u l d t h i n k o f 5-10 g r o u p s of power consumers t h a t a l l f o l l o wp r i n c i p a l l y t h e same model b u t w i t h a d i f f e r e n t p h a s i n g , and i t would t h e n b e i n t e r e s t i n g t o s t u d y n o t o n l y t h e t r a n s i t i o n s a s d e s c r i b e d by t h e model w i t h i n e a c h g r o u p , b u t a l s o t h e t r a n s i t i o n s between t h e g r o u p s . N e v e r t h e l e s s , t h e o b s e r v a t i o n s h a l l b e made h e r e t h a t t h e f o s s i l r e s e r v e s o f t h e g l o b e c o u l d b e j u s t s u f f i c i e n t f o r t r a n s i t i o n s , n o t f o r l o n g t e r n s t e a d y s t a t e s u p p l i e s , and t h e t i m e s c a l e f o r s u c h t r a n s i t i o n s c o u l d b e between 50 and
8 0 y e a r s . C o n s i d e r a t i o n s o f t h e k i n d t h a t a r e i n d i c a t e d by t h e model c o u l d a l s o b e u s e d
f o r t h e a s s e s s m e n t o f f u t u r e t e c h n o l o g i c a l developments and t h e t i m e s c a l e s t h a t must be imposed on them. Case 3 g i v e s t h e f i g u r e s f o r t h e 1 0 KW/capita c a s e . Simply a f a c t o r o f two i s g a i n e d .
2) A t t e n t i o n must b e drawn t o the l a r g e amounts of uranium t h a t a r e r e q u i r e d . F o r t h e model s o c i e t y o f 250 1 0 p e o p l e c o n s i d e r e d h e r e , t h i s u s e s up 6 a l l c h e a p uranium ( < $ 3 0 / l b ) t h a t seems t o be a v a i l a b l e on t h e g l o b e
.'
E x t r a p o l a t i o n t o 1 0 1 0 p e o p l e l e a d s i n t o p r i c e c l a s s e s o f uranium a s h i g h a s $ 1 0 0 - $ 2 0 o / l b . A s t h e overwhelming amount of t h i s uranium i s needed t o f u e l t h e LWR's,a l t e r n a t i v e c o n c e p t s have p r o b a b l y t o be e n v i s a g e d . T h e r e a r e many p o s s i b i l i t i e s f o r t h a t . To l o w e r t h e r e q u i r e d f a s t b r e e d e r i n v e n t o r y , f o r i n s t a n c e , by employing t h e c a r b i d e s a s f u e l i s one s u c h
p o s s i b i l i t y . (The v a l u e c o n s i d e r e d h e r e o f 3 to/GWe i s r a t h e r h i g h and r e f e r s t o t h e o x i d e b r e e d e r s . ) To i n c r e a s e t h e c o n v e r s i o n f a c t o r o f LWR's
and t h e r e b y t o p r o d u c e more t h a n 170 kg/GWe a i s a n o t h e r s u c h p o s s i b i l i t y . T h e r e a r e many more.
The model e n v i s a g e d h e r e c o u l d h e l p t o a s s e s s t h e v a r i o u s p r i o r i t i e s f o r s u c h d e v e l o p m e n t s i n t h e new l i g h t o f " R e a c t o r S t r a t e g i e s and t h e Energy C r i s i s . "
l ~ c c o r d i n g t o K . Hubbert El81
.
3) A t t e n t i o n must b e drawn t o t h e f a c t t h a t i n T a b l e 1 t h e Q ' s o f f o s s i l f u e l and t h e Q ' s f o r n a t u r a l uranium do n o t make up f o r t h e t o t a l e n e r g y consumption. The r e m a i n d e r i s t h e s h a r e o f t h e FBR's and t h e o p e r a t i o n o f t h e H T G R ' s . 4 ) Comparing c a s e s 1 and 2 a s w e l l a s c a s e s 3 and 4
p o i n t s t o t h e i n f l u e n c e o f t h e c a p a c i t y o f t h e n u c l e a r i n d u s t r y . F o r t a d i f f e r e n c e o f 15
E , 1
y e a r s a p p e a r s a n d , a s t h e f o s s i l f u e l c o n s u m ~ t i o n becomes l a r g e r , one a d d i t i o n a l Q i s r e q u i r e d f o r t h e model s o c i e t y G .
5 ) C a s e s 5 and 6 do n o t e x a c t l y meet t h e c o n d i t i o n s o f a c o m p l e t e l y c l o s e d Pu and
u~~~
b a l a n c e , b u t t h e y a r e c l o s e t o t h a t . They were d e s i g n e d t o have t h e same consumption o f f o s s i l f u e l , namely 3.97 Q . A r e d u c t i o n from 20 KW/capita t o 1 0 ~ W / c a p i t a i n c r e a s e s f o r s u c h f i x e d consumptions of f o s s i l f u e l t h e v a l u e o f t from 6 1 t o 82 y e a r s , a n dE , 1
r e q u i r e s o n l y one t h i r d o f n u c l e a r a n n u a l i n s t a l l m e n t . O r i n o t h e r words, s u c h d r a s t i c s a v i n g s o f e n e r g y p e r c a p i t a s t r e t c h e s t h e t i m e s c a l e f o r o n l y 2 1 y e a r s , t h e n w i t h 10 KW/capita t h e same problem a r i s e s a s i n t h e c a s e of 20 KW/
c a p i t a . I m p l i c i t i n t h i s r e a s o n i n g i s , of c o u r s e , t h a t t h e a s y m p t o t i c scheme o f F i g u r e 1 p r o v i d e s w i t h o u t d i f f i c u l t i e s e v e n v e r y l a r g e amounts o f
e n e r g y . I t should be k e p t i n mind, however, t h a t w h i l e t h e production i s n o t a problem t h e r e , t h e handling o f energy ( o r embedding) may v e r y w e l l pose a major problem C131. But t h i s i s n o t t h e p o i n t o f t h i s paper.
FIG. 3
POCYNOMlALS
TRANSIENT
POLYNOMlAL
\ *
I
0 .25 .SO 75 10
RELATIVE TlML
-
30-FIG. 4
POWER DISTRIBUTION FOR 20
KWth/CAPITA
GROWTH RATES INIT.( 1970) AVERAGE
PTOT
4 5Yo 2.7%-31-
FIG. 5 POWER DISTRIBUTION FOR 10Kyh /CAPITA
GROWTH ZATES INIT (1970) AVERAGE
PTOT
4 5 % 0.93%POPULATION : 1970 250MLL.
20W) 362 MILL.
LOO -
m-
-32-
FIG.6 STYLIZED MODEL
- 3 3 -
FlG.7 ANNUAL SEWRATIVE W M K
TIME IYEAIE 1
-34-
FIG.8 ANNUAL SEPARATIVE WORK
CUM= 1.83 x106 to SWU
0 X) 20 30 40 50 60 70
1970 )980 1990 Zoo0 20X) 20 20 2030 2040
TIME [YEARS 1
FIG.9 FOSSLL POWER REQUIREMENTS
ENERGY= 8 7 0
S""
P(t)dt = 3.94 Q1970 1980 1990 2000 2OlO 2020 2030 2040
TIME [YEARS]
10 K Wt I CAPITA A,= 18 GW/a
870 1980 1990 2000 20X) 2020 2030
TIME [YEARS]
R e f e r e n c e s
[
D i e t r i c h , J . R . " E f f i c i e n t U t i l i z a t i o n o f N u c l e a r F u e l s , " Power R e a c t o r T e c h n o l o q y ,6,
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6 ,
No. 5 ( 1 9 6 4 ) .[8] Grumm, H . e t a l . " K e r n b r e n n s t o f f b e d a r f und K o s t e n v e r s c h i e d e n e r R e a k t o r t y p e n i n D e u t s c h l a n d , "
K e r n f o r s c h u n g s z e n t r u m K a r l s r u h e , I n s t i t u t f u r Angewandte R e a k t o r p h y s i k , KFK 366, a n d
Ergtinzendes M a t e r i a l zum B e r i c h t ,
" K e r n b r e n n s t o f f b e d a r f und K o s t e n v e r s c h i e d e n e r R e a k t o r t y p e n i n D e u t s c h l a n d , " (KFK 366)
,
K e r n f o r s c h u n g s z e n t r u r n K a r l s r u h e , I n s t i t u t f u r Angewandte R e a k t o r p h y s i k , KFK 466.
[9] J a n s e n , P
.
"Methoden z u r B e u r t e i l u n g von K e r n k r a f t - w e r k s e n t w i c k l u n g e n , i n s b e s o n d e r e d e r S c h n e l l e n B r u t e r , " K e r n f o r s c h u n g s z e n t r u m K a r l s r u h e ,I n s t i t u t f u r Angewandte R e a k t o r p h y s i k , KFK 1066.
[lo]
H a r d e , R. a n d Memmert, G. " M o d e l l u n t e r s u c h u n g e n W e r A u s s i c h t e n und Konsequenzen d e r Verwendung von K e r n e n e r g i e z u r ElektrizitXtserzeugung,"A t o m w i r t s c h a f t , Band 11 ( 1 9 6 6 )
.
[ll] USAEC, " C o s t B e n e f i t A n a l y s i s o f t h e US B r e e d e r R e a c t o r Program, " D i v i s i o n o f R e a c t o r Develop- ment and T e c h n o l o g y , WASH 1 1 2 6 , A p r i l 1969.
" P o t e n t i a l N u c l e a r Power Growth P a t t e r n s , "
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Updated (1970) A n a l y s i s , WASH 1184.
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M a r c h e t t i , C . "Hydrogen and E n e r g y , " Chemical Economy and E n q i n e e r i n q Review ( J a n u a r y 1973) (Tokyo)
.
[IS] F o r t e s c u e , P. "A R e a c t o r S t r a t e g y : FBR1s and HTGR1s,"
N u c l e a r N e w s , 15,No. 4 ( A p r i l 1972)
.
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