ABSTRACTS

OPTIMIZATION V.

OF I. Kuz'min

FUEL

BREEDING

and

V.

Ya.

IN

REACTORS UDC 621.039.526

Pupko

T h e v a r i a t i o n a l p r o b l e m of d e t e r m i n i n g the m a x i m u m w, the i n i t i a l r a t e of i n c r e a s e of s e c o n d a r y _fuel, f o r a c o n s t a n t v a l u e of keff is c o n s i d e r e d . E u l e r ' s e q u a t i o n f r o m the c a l c u l u s of v a r i a t i o n s i s u s e d to find the o p t i m u m r a d i a t d i s t r i b u t i o n of P u 239 i n the c o r e . T h e v a r i a t i o n s of the f u n c t i o n a l s co a n d kef f a r e d e t e r m i n e d b y p e r t u r b a t i o n t h e o r y . The a l g o r i t h m u s e d in the n u m e r i c a l i t e r a t i o n m e t h o d p e r m i t s the r e d i s t r i b u t i o n of P u 239 c o n s i s t e n t with its e f f e c t i v e n e s s with r e s p e c t to co a n d kerr, t a k i n g a c c o u n t of c o n s t r a i n t s on the P u 23s c o n c e n t r a t i o n , and e n s u r e s the c o n v e r g e n c e of the s o l u t i o n . C o m p u t e r e a l c u I a t i o n s of the o p t i m u m P u 239 c o n c e n t r a t i o n s w e r e p e r f o r m e d i n the i S - g r o u p d i f f u s i o n a p p r o x i m a t i o n f o r a r e a c t o r of the BN-350 type. E x t r e m a of o t h e r f u n c t i o n a l s w e r e d e t e r m i n e d for c o r n p a r i s o n : KB r - the b r e e d i n g r a t i o for a r e a c t o r i n o n e - d i m e n s i o n a l c y l i n d r i c a l g e o m e t r y ; K r - the c o e f f i c i e n t d e s c r i b ing the r a d i a l v a r i a t i o n of heat r e l e a s e ; G 9 - the c h a r g e of I Pu 2~9 e n s u r i n g the g i v e n v a l u e of kef f. T a k i n g accoun~ only 5 of the c o n s t r a i n t s i m p o s e d on keff a n d the P u 2~9 c o n c e n t r a tion and the r e s t r i c t i o n s r e q u i r e d b y the p h y s i c a l n a t u r e of the p r o b l e m p e r m i t s an e s t i m a t e of the l i m i t i n g e f f e c t i v e n e s s of o p t i m i z a t i o n .

I

J T

2

[t i s c l e a r f r o m T a b l e 1 and Fig. 1 that o p t i m i z a t i o n with r e s p e c t to G9 a n d KB r l e a d s to P u 239 c o n c e n t r a t i o n s at the c e n t e r of the r e a c t o r which give r i s e to a n a b r u p t i n c r e a s e i n K r and t h e r e f o r e to a d e c r e a s e i n p o w e r . R e a c t o r s o p t i m i z e d with r e s p e c t to w and K r have n e a r l y the same parameters. It m a y b e p r e s u m e d that f l a t t e n i n g the heat r e l e a s e i n r e a c t o r s of the B N - 3 5 0 type will i n p r a c t i c e be a c c o m p a n i e d by o p t i m i z a t i o n with r e s p e c t to the r a t e of fuel b u i l d u p .

T A B L E 1. Ratio of R e a c t o r P a r a m e t e r s f o r O p t i m u m and U n i f o r m (with s u p e r s c r i p t 0) P u 239 C o n c e n t r a t i o n s naUve Alternative opti~um- mization o~/oJo

ol

Ito2

i

@ ~6 Core radius, tel. units

Fig. 1. O p t i m u m P u 239 d i s t r i b u t i o n s . N u m b e r s on c u r v e s c o r r e s p o n d to a l t e r n a t i v e o p t i m i z a t i o n s l i s t e d in T a b l e 1; p~ is the P u 23~ c o n c e n t r a t i o n f o r h o m o g e n e o u s loading.

i 2 3 4

] I

a~max, keff -- eonst Kr rain' keff = const G9rain, keft = const KBr max, kef t = const

%/a~ KBr/KB~r

t,44 0,64

t,08

t ,00

1;43 0 61

1,15

t ,00

0,26 [ 230

0,16

0,99

0,23 l 26',0 0,20

t,10

I

T r a n s l a t e d f r o m A t o m n a y a E n e r g i y a ' Vol. 28, No. 1, p. 47, J a n u a r y , 1970. m i t r e d F e b r u a r y 28, 1969; a b s t r a c t s u b m i t t e d J u l y 18, 1969.

Original article sub-

9 ConsHltants l~urea,~ a divisio~z of Plenu~t P,b!ishing Corporation, 227 I~'est 17th Street, '~ew York, N. }'. i0011. .Ill rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of t/~e publisI~er. '1 copy of this article is available /?om the publisher for $15.00.

50

INTERACTION

OF URANIUM

WITH

METAL

ALKALI

AND ITS

ALLOYS

FLUORIDES

G. P . N o v o s e l o v , I. a n d Y u . D. D o g a e v

N.

Kashcheev,

UDC 546.791

The fluoride method of r e p r o c e s s i n g i r r a d i a t e d metallic n u c l e a r fuel involves a l a r g e consumption of fluorine and substantial heat evolution [1]. A p r e l i m i n a r y conversion of metallic u r a n i u m to nonvolatile fluorides (UF4, UF3) and t h e i r further fluorination to the hexafluoride is expedient [2, 3]. The work p r e s e n t s the r e s u l t s of an investigation of the interaction of u r a n i u m with alkali metal fluorides at the t e m p e r a t u r e 1273~ and above under nonequilibrium conditions. It was established that u r a nium i n t e r a c t s with fluoride melts according to the reaction: U-~-nRF--~

['F n l-rill,

where R is an alkali metal (lithium, sodium, potassium); n is the valence of u r a n i u m (three o r four). The p r o c e s s e s are accompanied by an evolution of vapors of the alkali metals and the formation of u r a n i u m t e t r a and t rifluoride. F i g u r e ! p r e s e n t s the values of the rate of interaction of uranium with melts of m i x t u r e s of alkali metal fluorides and calcium fluoride of v a r i o u s compositions. Under these conditions calcium fluoride is an inert diluent. Thus, the amount of u r a n i u m that p a s sed into a CaF 2 melt at the t e m p e r a t u r e 1723~ in a period of 30 rain did not exceed 0.1%. With r e s p e c t to i n c r e a s i n g intensity of interaction with uranium, the alkali metal fluorides are a r ranged in the following sequence: L i F - N a F - - K F . The volatilities of these m e t a l s also i n c r e a s e in the same o r d e r , which indicates that the removal of t h e i r vapors f r o m the reaction zone is a deciding factor. In the case of a low content of alkali metal fluorides in the salt m i x t u r e s , the o r d e r of t h e i r a r r a n g e m e n t with r e s p e c t to intensity of i n t e r action is changed. In this case the p r o c e s s is limited by diffusion of the reaction components in the salt melt, and mixing of the salt i n c r e a s e s the rate of interaction of uranium with the reagent by ten-fold. It was shown that m e t a l s , the free e n e r g y of formation of whose fluorides is lower than that of u r a n i u m fluorides, interact with the salts m o r e intensively. F o r example, at the t e m p e r a ture 1373~ the rate of interaction of lanthanum with sodium fluoride was 9.2.10 -1 g / c m 2 . m i n , while that of uranium under the s a m e conditions was 8.2-10 -2 g / e m - m i n . Metals with a higher free energy of formation of fluorides (i ron, nickel, etc. ) negligibly interact with alkali metal fluorides. In the case of t r e a t m e n t of alloys of u r a n i u m with iron and nickel with sodium fluoride at 1523~ only the u r a n i u m interacted with the salt. LITERATURE 0 _20 ~0 60 Content of alkali metal fluoride in a mixture with CaF~% by weight Fig. 1. Dependence of the rate of interaction of uranium on the composition of the salt phase at the t e m p e r a t u r e 1523~

2.

CITED

N. P. Galkin et al., C h e m i s t r y and Technology of U r a nium Fluoride Compounds [in Russian], Gosatomizdat, Moscow (1961). G. P. Novoselov et al., "Interaction of u r a n i u m with alkali metal fluorides and t h e i r extraction of plutonium and f i s sion p r o d u c t s , " Report at the 36th Congress on Industrial C h e m i s t r y [in Russian], B r u s s e l s {1966).

T r a n s l a t e d f r o m Atonmaya E n e r g i y a , Vol. 28, No. 1, p. 48, J a n u a r y , 1970. mitted May 15, 1969; a b s t r a c t submitted October 2, 1969.

Original a r t i c l e sub-

51