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ORNL/TM-4210 Dist. C a t e g o r y UC-76

, C o n t r a c t No. W-7405-eng-26

CHEMICAL TECHNOLOGY D I V I S I O N

- - MULTIREGION

MRPP

_ -

PROCESSING PLANT CODE

C. W. K e e and L. E. M c N e e s e

SEPTEMBER

1976

-NOTICE

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION f o r the ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

iii

TABLE OF CONTENTS

Page No

........................... 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1 EQUATIONS AND ASSUMPTIONS . . . . . . . . . . . . . . . . . . . 3 2 . 1 Model f o r t h e Reactor . . . . . . . . . . . . . . . . . . 4 2.2 Model f o r t h e P r o c e s s i n g P l a n t . . . . . . . . . . . . . . 7 N W R I C A L METHODS EMPLOYED . . . . . . . . . . . . . . . . . . 13 3 . 1 S o l u t i o n of Reactor Material Balance Equations . . . . . . 1 3 3.2 S o l u t i o n of t h e P r o c e s s i n g P l a n t Material Balance 14 Equations . . . . . . . . . . . . . . . . . . . . . . . . 3.3 I t e r a t i o n w i t h Reactor Code . . . . . . . . . . . . . . . 15 3.4 C a l c u l a t i o n of Molar Volumes . . . . . . . . . . . . . . . 1 6 3.5 C o r r e c t i o n of D i s t r i b u t i o n C o e f f i c i e n t s . . . . . . . . . 1 7 3 . 6 I n v e s t i g a t i o n of F a s t e r S o l u t i o n Methods . . . . . . . . . 20 LIMITATIONS AND SPECIAL CONSIDERATIONS . . . . . . . . . . . . 2 1 4 . 1 L i m i t a t i o n s of Steady S t a t e C a l c u l a t i o n . . . . . . . . . 2 1 4.2 System of U n i t s . . . . . . . . . . . . . . . . . . . . . 22 4.3 D e s c r i p t i o n of P a r t i c u l a r Items Using Mass T r a n s f e r Coefficients . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Uses Requiring M o d i f i c a t i o n s . . . . . . . . . . . . . . . 23 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . 25 APPENDIX A: DESCRIPTION OF SUBROUTINES USED . . . . . . . . . 27 42 APPENDIX B: INPUT . . . . . . . . . . . . . . . . . . . . . . APPENDIX C: OUTPUT . . . . . . . . . . . . . . . . . . . . . . 60 ABSTRACT

MRPP

MULTIREGION PROCESSING PLANT CODE

C. W. b e and L. E. McNeese

ABSTRACT T h i s r e p o r t d e s c r i b e s t h e machine s o l u t i o n of a l a r g e number (% 52,000) of simultaneous l i n e a r a l g e b r a i c e q u a t i o n s i n which t h e unknowns are t h e c o n c e n t r a t i o n s of n u c l i d e s i n t h e f u e l s a l t of a f l u i d - f u e l e d r e a c t o r (MSBR) having a continuous f u e l p r o c e s s i n g p l a n t . Most of t h e e q u a t i o n s d e f i n e c o n c e n t r a t i o n s a t v a r i o u s p o i n t s i n t h e p r o c e s s i n g p l a n t . The code a l l o w s as i n p u t a g e n e r a l i z e d d e s c r i p t i o n of a p r o c e s s i n g p l a n t f l o w s h e e t ; i t a l s o performs t h e i t e r a t i v e adjustment of f l o w s h e e t parameters f o r d e t e r m i n a t i o n of c o n c e n t r a t i o n s throughout t h e f l o w s h e e t , and t h e a s s o c i a t e d e f f e c t of t h e s p e c i f i e d p r o c e s s i n g mode on t h e o v e r a l l r e a c t o r o p e r a t i o n .

INTRODUCTION

I n a r e a c t o r s u c h as a Molten-Salt Breeder Reactor f o r which continuous p r o c e s s i n g i s planned, t h e a b i l i t y t o compare a l t e r n a t e p r o c e s s i n g methods i s e s s e n t i a l i n determining t h e e f f e c t of small changes i n process i n g method on the s t e a d y - s t a t e o p e r a t i o n of a r e a c t o r and p r o c e s s i n g p l a n t . Because of t h e d e g r e e of i n t e r a c t i o n between t h e r e a c t o r performance and t h a t of t h e p r o c e s s i n g p l a n t , i t i s n e c e s s a r y t o c o n s i d e r t h e r e a c t o r and t h e p r o c e s s i n g system simultaneously.

The s h o r t c o o l i n g times r e s u l t i n g

from continuous p r o c e s s i n g cause a p p r e c i a b l e decay of n u c l i d e s i n t h e p r o c e s s i n g system and r e s u l t i n h i g h decay h e a t i n g rates and time-dependent chemical compositions.

Most p r o c e s s i n g p l a n t f l o w s h e e t s of i n t e r e s t , when

coupled c l o s e l y w i t h a r e a c t o r , produce numerous feedback streams t h a t

comp 1icat e m a t e r ia1 b a l a n c e c a l c u l a t i o n s and l e a d t o accumulation of

materials over long t i m e p e r i o d s .

To o b t a i n an a c c u r a t e r e p r e s e n t a t i o n

of t h e performance of t h e r e a c t o r and p r o c e s s i n g p l a n t i n such cases,

a flowsheet must be r e p r e s e n t e d i n d e t a i l , and a l a r g e r number of n u c l i d e s than considered p r e v i o u s l y must b e t a k e n i n t o account.

Computer programs have been developed and are d i s c u s s e d that a l l o w

a p r o c e s s i n g p l a n t and t h e a s s o c i a t e d r e a c t o r t o b e r e p r e s e n t e d i n such a manner t h a t the programs can be used i n d e p e n d e n t l y t o r e p r e s e n t e i t h e r t h e r e a c t o r o r p r o c e s s i n g p l a n t i n d e t a i l o r i n combination t o o b t a i n a d e t a i l e d r e p r e e e n t a t i o n o f t h e r e a c t o r and p r o c e s s i n g p l a n t system. Although each code s o l v e s a l a r g e system of simultaneous l i n e a r a l g e b r a i c e q u a t i o n s , because of t h e d i f f e r e n t c h a r a c t e r i s t i c s of t h e two systems, d i f f e r e n t methods of s o l u t i o n are u s e d ; b o t h methods were adapted f o r u s e w i t h s p a r s e matrices.

The r e a c t o r code u s e s a Gauss-Seidel i t e r a t i o n

t o s o l v e approximately 750 e q u a t i o n s . approximately 52,500 e q u a t i o n s .

The p r o c e s s i n g p l a n t code s o l v e s

However, a s p e c i a l o r d e r i n g scheme a l l o w s

a d i r e c t s o l u t i o n i n which t h e e q u a t i o n s are c o n s i d e r e d i n b l o c k s of 70 e q u a t i o n s each. The c a l c u l a t i o n s are c a r r i e d o u t i n an i t e r a t i v e manner between t h e r e a c t o r and t h e p r o c e s s i n g p l a n t f o r d e t e r m i n a t i o n of flowsheet parameters. These parameters i n c l u d e t h e molar d e n s i t y of p h a s e s i n each holdup v o l -

ume and t h e d i s t r i b u t i o n c o e f f i c i e n t s for each mass t r a n s f e r o p e r a t i o n i n t h e f l o w s h e e t ; t h i s f e a t u r e allows t h e s i m u l a t i o n of complw s t e p s i n a flowsheet by u s i n g e i t h e r an e q u i l i b r i u m o r f i r s t - o r d e r r a t e mechanism.

S e c t i o n s 2 through 4 of t h i s r e p o r t d i s c u s s t h e g e n e r a l problem and t h e set of e q u a t i o n s employed i n i t s s o l u t i o n , t h e method used f o r s o l u t i o n of t h e e q u a t i o n s , and t h e e x t e n s i o n s of t h e code t o s i m i l a r problems.

The appendixes e s s e n t i a l l y form a u s e r ' s manual and i n c l u d e

a d e s c r i p t i o n of t h e s u b r o u t i n e s , t h e i n p u t , and t h e o u t p u t from b o t h

t h e r e a c t o r and p r o c e s s i n g p l a n t codes.

A code l i s t i n g is a v a i l a b l e

from t h e a u t h o r s .

EQUATIONS AND ASSUMPTIONS

The m u l t i r e g i o n p r o c e s s i n g p l a n t code i s based on a model i n which

a MSBR and t h e a s s o c i a t e d p r o c e s s i n g p l a n t are r e p r e s e n t e d by s e p a r a t e r e g i o n s of uniform composition; allowance i s made f o r continuous flow between r e g i o n s , r a d i o a c t i v e decay of materials i n each r e g i o n , and t r a n s f e r of materials between r e g i o n s i n o r d e r t o r e p r e s e n t common m a s s t r a n s f e r effects.

Allowance is also made f o r f i s s i o n and n e u t r o n c a p t u r e r e a c t i o n s

i n regions representing the reactor.

The e q u a t i o n s which d e s c r i b e r e g i o n s

i n t h e p r o c e s s i n g p l a n t are similar t o t h o s e f o r the r e a c t o r ; however, t h e r e a c t o r i s r e p r e s e n t e d by a s e p a r a t e code, MATADOR,

which receives i n p u t

from a s i n g l e r e g i o n of the p r o c e s s i n g p l a n t ( t h e r e g i o n from which processed s a l t is returned t o t h e r e a c t o r ) .

The e q u a t i o n s f o r t h e p r o c e s s i n g

p l a n t are d e s c r i b e d s e p a r a t e l y from t h o s e f o r t h e r e a c t o r t o accommodate

the d i f f e r e n t assumptions t h a t are r e q u i r e d .

2.1

Model f o r t h e Reactor

A p r e v i o u s l y developed computer program, MATADOR, i s used f o r calc u l a t i o n of t h e c o n c e n t r a t i o n s of n u c l i d e s i n t h e primary c i r c u i t of a MSBR under s t e a d y - s t a t e c o n d i t i o n s i n which f u e l s a l t i s c o n t i n u o u s l y c i r c u l a t e d between t h e r e a c t o r and a p r o c e s s i n g system.

A s such, t h e pro-

gram serves as a s u b r o u t i n e t h a t c a l c u l a t e s t h e i n p u t f o r t h e p r o c e s s i n g p l a n t program ( i n t h e form of c o n c e n t r a t i o n s and flow r a t e of t h e s a l t t o b e p r o c e s s e d ) based on o u t p u t from t h e p r o c e s s i n g p l a n t ( i n t h e form of c o n c e n t r a t i o n s and flow rate of t h e processed s a l t t h a t i s r e t u r n e d t o the reactor).

F r o m t h e s t a n d p o i n t of t h e p r o c e s s i n g p l a n t program, t h e

r e a c t o r i s t r e a t e d as a s i n g l e r e g i o n ; however, t h e r e a c t o r program t r e a t s t h e r e a c t o r as a m u l t i r e g i o n system.

The e q u a t i o n s permit t h e u s e of

terms which are n o t n e c e s s a r y f o r e v e r y r e g i o n ; f o r example, flow of

material between any two r e g i o n s can be s p e c i f i e d , b u t t h i s seldom occurs. The e q u a t i o n s have been d e s c r i b e d p r e v i o u s l y Y 2 a l t h o u g h much of t h a t description i s repeated here. The accumulation rate of s p e c i e s i i n t h e f u e l s a l t i n t h e r e a c t o r i s t h e i n p u t r a t e of s p e c i e s i by f e e d , f i s s i o n , r a d i o a c t i v e decay, and n e u t r o n c a p t u r e i n t h e f u e l s a l t , g r a p h i t e , and c i r c u l a t i n g bubbles minus t h e d i s a p p e a r a n c e rate of s p e c i e s i due t o r a d i o a c t i v e decay, n e u t r o n c a p t u r e , d e p o s i t i o n on exchanger s u r f a c e s , and chemical p r o c e s s i n g . s t e a d y s t a t e , t h i s r a t e of accumulation i s z e r o , s o t h a t :

where

2 s u r f a c e area of c i r c u l a t i n g b u b b l e s , cm ,

A g

2 s u r f a c e area of g r a p h i t e , an ,

v o l u m e t r i c flow rate of f u e l s a l t t o t h e r e a c t o r , c c / s e c ,

c o e f f i c i e n t f o r loss of s p e c i e s i by d i f f u s i o n i n t o

g r a p h i t e , un/sec, Hi

c o e f f i c i e n t f o r loss of s p e c i e s i by m i g r a t i o n t o bubbles,

cm/sec, pi 'i

e f f e c t i v e chemical p r o c e s s i n g rate f o r s p e c i e s i , c c / s e c ,

rate a t which s p e c i e s i p l a t e s on t h e h e a t exchanger s u r f aces , cm/sec,

v vC C

e..

volume of f u e l s a l t , c c ,

volume of f u e l s a l t i n c o r e , c c ,

c o n c e n t r a t i o n of s p e c i e s i, moles/cc,

f e e d c o n c e n t r a t i o n of s p e c i e s i, moles/cc,

f r a c t i o n of d i s i n t e g r a t i o n s by s p e c i e s j which l e a d s t o

formation of s p e c i e s i ,

f r a c t i o n of n e u t r o n c a p t u r e s by s p e c i e s j which l e a d s t o f o r m a t i o n of s p e c i e s i,

gij

c o e f f i c i e n t f o r p r o d u c t i o n of s p e c i e s i by d i f f u s i o n of s p e c i e s j i n t o g r a p h i t e , cm/sec,

c o e f f i c i e n t f o r p r o d u c t i o n of s p e c i e s i by m i g r a t i o n of s p e c i e s j t o g a s b u b b l e s , cm/sec,

sij

rate of p r o d u c t i o n of s p e c i e s i from s p e c i e s j p l a t e d on t h e heat exchanger s u r f a c e s , c c / s e c ,

Yij

f i s s i o n y i e l d of s p e c i e s i from f i s s i o n of s p e c i e s j ,

12I â&#x20AC;&#x2DC;i

â&#x20AC;&#x2DC;fi

-I

r a d i o a c t i v e d i s i n t e g r a t i o n c o n s t a n t of s p e c i e s i , sec

average neutron-capture c r o s s s e c t i o n of s p e c i e s i , cm

2 average f i s s i o n c r o s s s e c t i o n of s p e c i e s i , cm ,

-2 -1 average n e u t r o n f l u x , cm see

Thus, f o r I n u c l i d e s , t h i s e q u a t i o n i s a system of I simultaneous a l g e b r a i c e q u a t i o n s and I unknowns. unknowns are considered by:

Two o t h e r s e t s of I e q u a t i o n s and I

(1) allowing f o r a volume of gas bubbles and

a holdup f o r materials p l a t e d o u t i n t h e r e a c t o r f l u x , and (2) allowing a r e g i o n i n which t h e e v o l v i n g g a s bubbles and t h e materials p l a t e d o u t o u t s i d e t h e r e a c t o r c o r e are h e l d i n c o n t a c t w i t h f u e l s a l t so t h a t s o l u b l e decay p r o d u c t s may be r e t u r n e d t o the r e a c t o r . A l l t h r e e sets of I e q u a t i o n s are s o l v e d by t h e Gauss-Seidel

s u c c e s s i v e s u b s t i t u t i o n a l g o r i t h m , w i t h i t e r a t i o n o c c u r r i n g over each of t h e s u c c e s s i v e sets of I e q u a t i o n s .

Because of the s i z e of t h e

d i a g o n a l terms, t h e system of e q u a t i o n s converges r a p i d l y .

Direct s o l -

u t i o n s were n o t used because of t h e s t o r a g e r e q u i r e d f o r remembering a c o e f f i c i e n t matrix. The t r e a t m e n t of d i f f u s i o n of n o b l e g a s e s i n t o and decay p r o d u c t s This o u t of t h e g r a p h i t e u s e s a model developed by Kedl and H ~ u t z e e l . ~ model assumes that the g r a p h i t e moderator i s r e p l a c e d by s e m i - i n f i n i t e s o l i d c y l i n d e r s w i t h t h e same surface-to-volume

r a t i o , and t h a t t h e

g r a p h i t e i s c o a t e d w i t h a low p e r m e a b i l i t y material t o a d e p t h of l m i l . D i f f u s i o n of n o b l e g a s e s i n t o t h e g r a p h i t e o c c u r s through a l i q u i d f i l m and t h e c o a t i n g , and i s s i m u l a t e d by a lumped r e s i s t a n c e model.

The

model developed f o r t h e m i g r a t i o n o f n o b l e g a s e s and n o b l e metals t o c i r c u l a t i n g helium bubbles i s an e x t e n s i o n of t h e model proposed by Kedl and Houtzeel.3

Both of t h e s e models are d e s c r i b e d i n r e f . 2.

Once t h e set of c o n c e n t r a t i o n s i s o b t a i n e d , i t i s p o s s i b l e t o calc u l a t e h e a t g e n e r a t i o n r a t e s , f i s s i o n product p o i s o n i n g , p r o d u c t i o n r a t e s of t h e materials i n t h e r e a c t o r , i n v e n t o r y i n moles of t h e m a t e r i a l i n

t h e r e a c t o r , t h e uranium mole f r a c t i o n , and t h e b r e e d i n g r a t i o .

The

breeding r a t i o i s c a l c u l a t e d by assuming t h a t i t varies l i n e a r l y v i t h small changes i n t h e f i s s i o n product poisoning.

Thus, t h e breeding r a t i o

i s determined from t h e d i f f e r e n c e between t h e r e f e r e n c e f i s s i o n product p o i s o n i n g (from ROD4 c a l c u l a t i o n s ) and t h e c a l c u l a t e d f i s s i o n product poisoning. I n c a l c u l a t i n g t h e f i s s i o n product p o i s o n i n g , the poisoning from 135Xe

i s excluded because i t w a s a l s o excluded i n t h e r e a c t o r d e s i g n code,

ROD, where i t w a s always assumed t o be one-half

of 1%.While MATADOR

c a l c u l a t i o n s of f i s s i o n p r o d u c t poisoning i n c l u d e a b s o r p t i o n s by t h e n o b l e g a s e s and n o b l e metals i n t h e gas b u b b l e s , n o b l e metals p l a t e d o n t o s u r f a c e s o u t s i d e the r e a c t o r c o r e are n o t assumed t o absorb n e u t r o n s . Neptunium a b s o r p t i o n s are i n c l u d e d , because the r e f e r e n c e f i s s i o n product p o i s o n i n g used by ROD from p r e v i o u s c a l c u l a t i o n s i n c l u d e d t h e neptunium

a b s o r p t i o n s w i t h f i s s i o n p r o d u c t poisoning.

2.2

Model f o r the P r o c e s s i n g P l a n t

The p r o c e s s i n g p l a n t code c a l c u l a t e s s t e a d y - s t a t e

concentrations

based on material b a l a n c e e q u a t i o n s , and c o n s t a n t r e a c t o r e f f l u e n t concent r a t i o n s as determined by t h e l a s t MATADOR c a l c u l a t i o n .

The m u l t i r e g i o n

code assumes t h a t t h e p r o c e s s i n g p l a n t i s composed of a number of r e g i o n s ( o r holdup volumes) connected by flowing streams.

A r e g i o n c o n s i s t s of

a well-mixed volume c o n t a i n i n g one o r two phases i n e q u i l i b r i u m .

The

e q u i l i b r i u m i s s p e c i f i e d by a p r o p o r t i o n a l i t y c o n s t a n t t h a t v a r i e s w i t h atomic number and may be changed between s u c c e s s i v e flowsheet c a l c u l a tions.

Any two r e g i o n s may b e l i n k e d by flowing streams o r by r a t e

e x p r e s s i o n s , and each r e g i o n may have f e e d s o r d i s c a r d s .

(These are

streams which do n o t connect two r e g i o n s i n t h e p l a n t . ) 2.2.1

Material b a l a n c e e q u a t i o n s

The r a t e of accumulation of n u c l i d e i i n a r e g i o n (0 a t s t e a d y s t a t e ) i s t h e r a t e of appearance of i i n t h e r e g i o n from f e e d streams, from flowing streams from o t h e r r e g i o n s , from m a s s t r a n s f e r from o t h e r r e g i o n s , and from p r o d u c t i o n of o t h e r n u c l i d e s by r a d i o a c t i v e decay minus t h e rate of d i s a p p e a r a n c e of i from t h e r e g i o n by flow o u t , by m a s s t r a n s f e r t o o t h e r r e g i o n s , and by r a d i o a c t i v e decay. s t e a d y state i n r e g i o n n : =

jSi

FSm,n

+ Kj , n V B,n ) cj , n

'jeij('S,n

,m +

m m#n

F m , n Ki , m c i , m

m m#n

m#n

-C

'i('S,n

Sn,m i- DSn

K i , n 'B,n)

+K.

r,n

C F

'i,n

FIi,n

Thus, a t

where =

DSn

Sm,n

FIi,n K

i,n

flow rate of phase S from r e g i o n m t o r e g i o n n , cm / s e c , f e e d r a t e of n u c l i d e i t o r e g i o n n , m o l e s / s e c , d i s t r i b u t i o n r a t i o f o r nuclide i i n region n , volume of phase S i n r e g i o n n , c c ,

'Sn C

3 d i s c a r d r a t e of phase S from r e g i o n n , cm / s e c ,

c o n c e n t r a t i o n of n u c l i d e i i n f i r s t phase of r e g i o n n ,

i,n

moles/cc,

f r a c t i o n s of d i s i n t e g r a t i o n s of s p e c i e s j which l e a d t o

formation of s p e c i e s i, (kia)m,n

mass t r a n s f e r r a t e c o n s t a n t f o r t r a n s f e r of s p e c i e s i

from r e g i o n m t o region n , cm / s e c [ t h e r a t i o of ( k . a ) I

and (kia)

n,m

m,n

i s a d i s t r i b u t i o n f u n c t i o n , as d i s c u s s e d

i n Sect. 2 . 2 . 2 1 ,

decay c o n s t a n t f o r n u c l i d e i , s e c

s u b s c r i p t s B and S

-1 , and

phases

i and j = n u c l i d e s m and n = r e g i o n s .

Hence, t h e r e i s one e q u a t i o n and one unknown f o r each n u c l i d e i n each region.

There are 52,500 e q u a t i o n s f o r 750 n u c l i d e s i n 70 r e g i o n s .

Because of t h e number of e q u a t i o n s and t h e number and s i z e of r e c y c l e

streams p r e s e n t i n a f l o w s h e e t , t h e Gauss-Seidel i t e r a t i o n i s t o o time consuming.

S i n c e n e u t r o n c a p t u r e s are n e g l e c t e d , i t i s p o s s i b l e t o

a r r a n g e t h e n u c l i d e s s o t h a t e a c h n u c l i d e p r e c e d e s a l l of i t s decav daughters.

For N r e g i o n s , t h e r e i s one set of N e q u a t i o n s w i t h N unknowns

f o r each n u c l i d e .

By a r r a n g i n g t h e n u c l i d e s i n t h e p r o p e r o r d e r and

s o l v i n g each s e t of e q u a t i o n s , a d i r e c t s o l u t i o n f o r t h e e n t i r e set of equations is obtained.

S o l u t i o n s i n t h e p r o c e s s i n g p l a n t are a l t e r n a t e d

w i t h c a l l s t o MATADOR t o o b t a i n a converged s o l u t i o n f o r a r e a c t o r coupled with continuous p r o c e s s i n g . The program used h a s been designed t o s o l v e a l a r g e system of e q u a t i o n s i n which t h e n o n t r i a n g u l a r c o e f f i c i e n t matrix may be expressed

as a lower t r i a n g u l a r c o e f f i c i e n t matrix whose elements are m a t r i c e s . Each matrix on t h e d i a g o n a l i s s o l v e d d i r e c t l y , w i t h s u b s t i t u t i o n s b e i n g made f o r unknowns t h a t were c a l c u l a t e d p r e v i o u s l y .

In t h i s case, t h e

lower t r i a n g u l a r matrix h a s o f f - d i a g o n a l terms i n row i and column j of t h e form:

A . eij V

where V %j

d i a g o n a l m a t r i x w i t h t h e n t h term on t h e d i a g o n a l being + K

' S n

j ,n 'Bn

The terms on t h e d i a g o n a l ( i = j ) are matrices of the form: R.

hi&

R. i s a m a t r i x whose element i n row n and column m i s

where

= 1 i f n=m, and

n,m n3m

0 i f nfm.

The r e s u l t i n g system of e q u a t i o n s , when used w i t h a c o n s t a n t v e c t o r i n d i c a t i n g f e e d streams, i s t h e s e t of E q s . ( 2 ) .

2.2.2

Mass t r a n s f e r c o e f f i c i e n t s

Three models w e r e used f o r mass t r a n s f e r between l i q u i d and gas For t r a n s f e r of n o b l e g a s e s t o gas bubbles, t h e o v e r a l l l i q u i d

phases.

m a s s t r a n s f e r c o e f f i c i e n t was e s t i m a t e d from t h e Hughmark c o r r e l a t i o n g i v e n by S c h a f t l e i n and Russell.’

This i s s u b s t i t u t e d i n t o t h e r e l a t i o n

f o r mass t r a n s f e r : Ni

= KOLA&

KoL%cR

- KoL$H

cg’

where 2

= bubble s u r f a c e area,

= Henry’s l a w c o n s t a n t , m o l e s / c c (liq) p e r mole/cc ( g a s ) ,

KoL Ni

cR and c

= o v e r a l l l i q u i d m a s s t r a n s f e r c o e f f i c i e n t , cm/sec, =

rate of m a s s t r a n s f e r , m o l e s / s e c ,

= c o n c e n t r a t i o n s i n l i q u i d and g a s , moles/cc.

T h i s e q u a t i o n is broken i n t o two c o n t r i b u t i o n s to matrix terms analogous t o a flow rate so that:

(kia)m,n

ICoL

H = H(k a) i n,m’

where r e g i o n n i s t h e l i q u i d phase, and r e g i o n m the g a s phase. I n a d d i t i o n t o t h i s t r a n s f e r , the r a t e of m a s s t r a n s f e r a t t h e s u r f a c e between the l i q u i d and cover g a s must a l s o b e considered.

For

v o l a t i l e components, the mass t r a n s f e r r e s i s t a n c e i s assumed t o b e a c r o s s a l i q u i d f i l m of t h i c k n e s s XR:

Ni =

DRAs (ca

- Hcg)

= D 9, Ag

-DRAsH

(5)

where 2

DE = d i f f u s i v i t y i n l i q u i d , cm /sec, 2 As = s u r f a c e area, cm ;

thus, (kia)n ,m = (DRAB /Xa

The same model i s used t o d e s c r i b e t r a n s f e r of n o n v o l a t i l e decay p r o d u c t s of v o l a t i l e f i s s i o n p r o d u c t s a c r o s s a g a s f i l m of t h i c k n e s s X

gâ&#x20AC;&#x2122;

however,

s i n c e t h e t r a n s f e r from l i q u i d t o g a s i s z e r o , t h e r e i s o n l y one term. A l l of t h e s e terms must be added t o o b t a i n t h e m a t r i x c o e f f i c i e n t s t h a t

are used. I n both models t h e d e s i g n c r i t e r i o n i s based on some c o n s i d e r a t i o n

o t h e r than t h e removal of v o l a t i l e n u c l i d e s .

For example, t h e g a s rate

might b e based on t h e amount of r e d u c t a n t n e c e s s a r y f o r a h y d r o f l u o r i n a t o r o r a hydrogen-sparged probe i n a s u r g e tank.

v e s s e l , o r on t h e amount of argon needed f o r a level I n a f l u o r i n a t o r , however, t h e d e s i g n i s chosen

t o a c h i e v e a s p e c i f i e d performance such as p e r c e n t removal of uranium. For z e r o i n l e t c o n c e n t r a t i o n i n t h e g a s , a material b a l a n c e g i v e s : F c = F c L I G G

FLcL = P RF Lc I

FLcL,

13 V

where F~ , F ~ C

I’CL’CG

f l o w rates i n l i q u i d and g a s , c c / s e c ,

c o n c e n t r a t i o n s i n i n l e t l i q u i d , o u t l e t l i q u i d , and out l e t gas

PR =

moles / c c ,

p e r c e n t removal;

thus, the transfer across the interface is P

I’

S u b s t i t u t i n g for

: D

In the s i m u l a t i o n , F

element, and P R / ( l

w a s i n c l u d e d as a parameter independent of t h e

- PR) w a s

l i s t e d as a c o n s t a n t t h a t depended on t h e

element number.

3. 3.1

NUMERICAL METHODS EMPLOYED

S o l u t i o n of Reactor Material Balance Equations

The number of e q u a t i o n s t o b e s o l v e d by t h e r e a c t o r code i s e q u a l

t o the number of n u c l i d e s , Y 7 3 9 .

T h e coupling of t h e e q u a t i o n s used for

t h e s a l t i n t h e d r a i n t a n k with t h o s e used f o r t h e gas bubbles adds two a d d i t i o n a l sets of t h e same number of e q u a t i o n s .

The d i r e c t s o l u t i o n

of such a s e t of e q u a t i o n s would r e q u i r e a m e t h o d that would take advant a g e of s p a r s e n e s s and might need o n l y l i m i t e d p i v o t i n g t o minimize f i l l . These problems are e l i m i n a t e d by t h e u s e of an iterative s o l u t i o n , prov i d i n g t h e s o l u t i o n i s o b t a i n e d i n a r e a s o n a b l e number of i t e r a t i o n s . The number of i t e r a t i o n s has always been less than 30.

3.2

S o l u t i o n of t h e P r o c e s s i n g P l a n t Material Balance Equations

The number of e q u a t i o n s and unknowns f o r a flowsheet of 70 r e g i o n s and a n u c l e a r l i b r a r y of 739 n u c l i d e s i s about 52,000.

S t o r a g e of t h e

c o e f f i c i e n t matrix of t h i s system of e q u a t i o n s i s completely i m p r a c t i c a l , and s t o r a g e of even t h e nonzero terms could e a s i l y exceed t h e s t o r a g e c a p a c i t y of machines a v a i l a b l e ; t h e r e f o r e , a d i r e c t Gauss r e d u c t i o n could n o t be used. iteration.

Various approaches were made by u s i n g a Gauss-Seidel

The b e s t method w a s found t o b e a series of s o l u t i o n s f o r

a l l n u c l i d e c o n c e n t r a t i o n s i n the f l o w s h e e t ; t h e n u c l i d e s w e r e considered one a t a time s o t h a t some n u c l i d e s r e q u i r e d o n l y a f e w i t e r a t i o n s .

Even

w i t h t h e rearrangement of n u c l i d e s , which n e c e s s i t a t e d only one s o l u t i o n f o r each s p e c i e s , t h e t i m e requirements w e r e s t i l l e x c e s s i v e ; t h i s w a s because t h e d i a g o n a l element of t h e c o e f f i c i e n t matrices w a s comparable i n magnitude t o t h e off-diagonal terms, e x c e p t f o r n u c l i d e s w i t h s h o r t half -lives. For each s u c c e s s i v e n u c l i d e , a 70 by 70 m a t r i x w a s s o l v e d t o o b t a i n t h e c o n c e n t r a t i o n of t h a t n u c l i d e i n each of 70 r e g i o n s .

The time

requirement f o r a d i r e c t s o l u t i o n f o r a l l c o n c e n t r a t i o n s i n the p r o c e s s i n g p l a n t by t h i s method w a s q u i t e r e a s o n a b l e IBM 360/91.

less t h a n a minute f o r t h e

I n a d d i t i o n , t h e memory r e q u i r e m e n t s w e r e e s s e n t i a l l y t h e

same as t h o s e f o r t h e i t e r a t i o n technique.

The s t o r a g e of t h e s o l u t i o n

v e c t o r i s a s i g n i f i c a n t f r a c t i o n of t h e s t o r a g e r e q u i r e m e n t , and f o r l a r g e r f l o w s h e e t s (the IBM 360/91 a t ORNL w a s a b l e t o h a n d l e 250 r e g i o n s ) t h e s o l u t i o n v e c t o r uses most of t h e s t o r a g e .

15 V

3.3

I t e r a t i o n w i t h Reactor Code

The e x i s t e n c e of t h i s reasonably r a p i d s o l u t i o n f o r t h e p r o c e s s i n g p l a n t c a l c u l a t i o n enabled i t e r a t i o n s w i t h t h e MATADOR r o u t i n e which s i m u l a t e d t h e r e a c t o r performance.

MATADOR w a s coupled t o t h e p r o c e s s i n g

p l a n t c a l c u l a t i o n by u s i n g removal times d e f i n e d as the r e a c t o r i n v e n t o r y of a s p e c i e s d i v i d e d by i t s n e t removal rate by chemical p r o c e s s i n g . F a i r l y r a p i d convergence of c o n c e n t r a t i o n s w a s achieved f o r most n u c l i d e s i f t h e p a r a m e t e r s that passed between r o u t i n e s were averaged w i t h t h e i r p r e v i o u s v a l u e s t o p r o v i d e damping.

20 i t e r a t i o n s .

All c o n c e n t r a t i o n s converged w i t h i n

However, t h e v a r i a t i o n of more parameters between i t e r a -

t i o n s , and t h e c o n s i d e r a t i o n of more d i f f i c u l t f l o w s h e e t s r e q u i r e d improvement t o t h e code.

The u s e of r e a c t o r i n l e t c o n c e n t r a t i o n s r a t h e r

than removal times r e s u l t e d i n comparable performance, b u t p e r m i t t e d a d i f f e r e n t set of n u c l i d e s t o converge r a p i d l y .

Hence, the c o n c e n t r a t i o n s

i n the stream r e t u r n i n g t o t h e r e a c t o r can be d e s c r i b e d as t h e sum of t h e amount remaining a f t e r p r o c e s s i n g and t h e amount due t o p r o d u c t i o n i n the processing plant. At the same t i m e t h e s o l u t i o n i s found f o r t h e p r o c e s s i n g p l a n t c o n c e n t r a t i o n s , a s o l u t i o n i s also found f o r t h e f i r s t d e r i v a t i v e of the r e a c t o r i n l e t c o n c e n t r a t i o n w i t h r e s p e c t t o t h e o u t l e t concentra-

t i o n of t h e same n u c l i d e .

T h i s i s p o s s i b l e because t h e same c o e f f i c i e n t

m a t r i x i s used f o r b o t h sets of e q u a t i o n s .

The c o n s t a n t v e c t o r i n t h e

s o l u t i o n f o r t h e d e r i v a t i v e i s a v e c t o r w i t h u n i t c o n c e n t r a t i o n of each n u c l i d e i n t h e r e a c t o r and no terms f o r p r o d u c t i o n by decay.

Hence,

w i t h l i t t l e i n c r e a s e i n c a l c u l a t i o n a l e f f o r t and complexity, p r o v i s i o n

can be made f o r small changes i n c o n c e n t r a t i o n t o a l l o w t h e r e a c t o r code t o p r e d i c t t h e p r o c e s s i n g p l a n t performance.

I n a d d i t i o n , an even

g r e a t e r s a v i n g of t i m e i s made by c o n s i d e r i n g o n l y t h o s e n u c l i d e s whose c o n c e n t r a t i o n s are slowly converging, and by p e r i o d i c a l l y r e c o n s i d e r i n g

a l l nuclides. 3.4

C a l c u l a t i o n of Molar Volumes

The s t e a d y - s t a t e performance of a p r o c e s s i n g p l a n t depends on t h e

rates of decay and, t h e r e f o r e , t h e molar i n v e n t o r i e s of r a d i o a c t i v e n u c l i d e s throughout t h e p r o c e s s i n g p l a n t .

It i s t h u s n e c e s s a r y f o r t h e

molar i n v e n t o r i e s and molar volumes t o be c o n s i s t e n t with t h e volumes specified.

It i s a l s o n e c e s s a r y t o know t h e r a t i o of t h e molar volumes

of t h e two phases i n c e r t a i n r e g i o n s f o r u s e as a conversion f a c t o r t o c o n v e r t t h e d i s t r i b u t i o n c o e f f i c i e n t s from r a t i o s of mole f r a c t i o n t o t h e r a t i o of c o n c e n t r a t i o n s i n moles p e r c u b i c c e n t i m e t e r .

T h i s problem

i s n o t a l l e v i a t e d by u s e of molar flow rates and mole f r a c t i o n s , because

the parameters must be such t h a t t h e mole f r a c t i o n s add up t o 1.0. Between i t e r a t i o n s , each f l o w rate from a r e g i o n i s expressed as

a f r a c t i o n of t h e t o t a l f l o w from t h a t r e g i o n .

The molar volume of each

stream f o r which a molar volume c o r r e c t i o n i s t o b e made i s determined by assuming a d d i t i v e molar volumes.

The c o r r e c t e d f l o w r a t e i s g i v e n

by t h e p r o d u c t of t h i s molar volume; t h e molar f l o w rate and the r a t i o of molar volumes f o r r e g i o n s c o n t a i n i n g s a l t and bismuth p r o v i d e s a conversion f a c t o r f o r t h e d i s t r i b u t i o n c o e f f i c i e n t s .

C o r r e c t i o n of D i s t r i b u t i o n C o e f f i c i e n t s

3.5

For a g i v e n r e g i o n n , t h e set of c o n c e n t r a t i o n s of t h a t r e g i o n i s the solution of: 'iVS,n

[FS

(INPUT)

Ki,n(FB

hiVB,njCi,n = j

j ei j ('S,n

+ K

V )c j , n B,n j , n

i ,n

where

FSn,m

(INPUT)

+ Dn,

and

= t o t a l i n p u t of n u c l i d e i t o r e g i o n n from f e e d s o r o t h e r

i ,n

regions. From a t a b l e of v a l e n c e s , i t is p o s s i b l e t o c a l c u l a t e an e q u i v a l e n t d e n s i t y i n t h e second phase i n e q u i v a l e n t s p e r c u b i c c e n t i m e t e r .

It i s

t h i s number which must remain c o n s t a n t through any series of r e d u c t i v e e x t r a c t i o n o p e r a t i o n s t o s a t i s f y t h e c o n d i t i o n of an e q u i v a l e n t balance. The e q u i v a l e n t d e n s i t y , E

i n the second phase t h a t e n t e r s the r e g i o n

may b e a c a l c u l a t e d v a r i a b l e o r an i n p u t v a r i a b l e . variable D

E - E

%i,n

I n e i t h e r case, t h e

must be determined s o t h a t

"0,

where = C(VAL)i E = E E i iYn i

KiYn

ciYn = t o t a l number of e q u i v a l e n t s p e r

m i l l i l i t e r i n t h e bismuth p h a s e , and (VAL)i = v a l e n c e of i i n s a l t .

We have a l s o d e f i n e d :

since

where A and A are c o n s t a n t s . n C The p r o p e r v a l u e of DLi

can b e found i t e r a t i v e l y by Newton's method

i f w e have a means f o r e v a l u a t i n g

Although the s p e c i f i c d e r i v a t i v e may b e found, an approximation i s g i v e n because i t r e q u i r e s less time and memory, i n v o l v e s terms a l l of the same s i g n , and s t i l l arrives a t t h e p r o p e r DLi. t h e c o n s t a n t terms:

A1 A2

+ Ai

Ai V V

S ,n

B ,n

so that (PROD)

(PROD)i K i ,n (VAL)i E

i ,n

A~ + Ki ,nA2

By o b t a i n i n g t h e d e r i v a t i v e of E

from Eq. (12):

It i s convenient t o r e d e f i n e

dEi ,n

= (PROD) (VAL)

d Di~

+ Ki ,nA2

KipnA2 21 ( A ~ K~ , , A ~ )

assuming t h a t (PROD) i s independent of DL i

dKi,n dDLi

(14)

While t h i s assumption i s

*n AnAcDLi = -An K. DLi DLi 1,n for DLi

# 0

then

i,n

(

Kiyn2

(16)

DLi

Thus, as c a l c u l a t i o n s are made f o r E = C Ei , n â&#x20AC;&#x2122; c a l c u l a t i o n s are e a s i l y made f o r

f o r u s e in t h e n e x t i t e r a t i o n can b e o b t a i n e d by allowing

The p r o p e r DLi convergence of

(DLilel

(DLilm

Eo)

dDLi S i n c e (PROD).1 i s dependent upon DLi,

two terms have been l e f t o u t .

Some p r o v i s i o n must a l s o be made f o r the f a i l u r e of t h i s scheme t o converge. The c a l c u l a t i o n procedure examines t h e s i g n of E u o u s l y s p e c i f y upper and lower bounds f o r DLi.

E 0 i n o r d e r t o contin-

Any new DLi v a l u e t h a t

i s o u t s i d e t h i s i n t e r v a l i s r e p l a c e d w i t h t h e v a l u e a t t h e midpoint of the interval.

T h i s v a l u e of DLi might t e n d t o o v e r c o r r e c t i n a f l o w s h e e t ,

e s p e c i a l l y i f t h e s e r e g i o n s are i n series.

As a means of p r o v i d i n g a

damping e f f e c t , t h e v a l u e r e t u r n e d f o r t h e n e x t i t e r a t i o n i s a weighted average of t h i s v a l u e and t h e o l d v a l u e .

3.6

I n v e s t i g a t i o n of F a s t e r S o l u t i o n Methods

When flowsheet parameters such as flow rates ( i . e . , molar volume) and d i s t r i b u t i o n c o n s t a n t s are n o t changed between i t e r a t i o n s , t h e solution f o r a l l b u t t h e f i r s t i t e r a t i o n can be speeded up.

The s o l u t i o n

by r e d u c t i o n and back s u b s t i t u t i o n i s a series of row o p e r a t i o n s on an augmented matrix; much of t h e c a l c u l a t i o n a l time i s used t o perform o p e r a t i o n s on t h e c o e f f i c i e n t m a t r i x .

For double p r e c i s i o n c a l c u l a t i o n s ,

t h e i n f o r m a t i o n r e q u i r e d f o r making t h e n e c e s s a r y row o p e r a t i o n on o n l y t h e c o n s t a n t v e c t o r i s a double p r e c i s i o n c o n s t a n t and two i n d e x e s which i n d i c a t e t h e rows involved.

T h i s i n f o r m a t i o n can b e s t o r e d e a s i l y i n

t h e e l i m i n a t e d matrix p o s i t i o n s d u r i n g the f i r s t i t e r a t i o n s o t h a t t h e y may be used on subsequent i t e r a t i o n s .

The c a l c u l a t i o n s after t h e f i r s t

i t e r a t i o n are m a n i p u l a t i o n s performed on a v e c t o r r a t h e r than o p e r a t i o n s

on a matrix; i n a d d i t i o n , t h e matrix, which i s n o t r e q u i r e d , need n o t b e determined i n t h e s e subsequent i t e r a t i o n s . Before t h e i n t r o d u c t i o n of changing flowsheet p a r a m e t e r s , t h e number of row o p e r a t i o n s r e q u i r e d f o r a 50 by 50 f l o w s h e e t m a t r i x w a s determined.

Between 200 and 280 row o p e r a t i o n s w e r e p e r f o m e d w i t h

about 80% of t h e c a l c u l a t i o n a l t i m e r e q u i r e d f o r O p e r a t i o n s on t h e c o e f f i c i e n t matrix.

The number of c o n s t a n t s needed f o r a l l n u c l i d e s

r e q u i r e s more memory t h a n i s a v a i l a b l e as f a s t memory; however, because t h e c o n s t a n t s need o n l y be accessed s e q u e n t i a l l y , s t o r a g e on a d i r e c t a c c e s s d e v i c e is s u f f i c i e n t , and o n l y a small b u f f e r s p a c e i s r e q u i r e d .

LIMITATIONS AND SPECIAL CONSIDERATIONS

4.1

L i m i t a t i o n s of Steady S t a t e C a l c u l a t i o n

A number of problems arise from t h e c o n s i d e r a t i o n of a s t e a d y s t a t e process ( i . e . ,

f l o w s h e e t s t e p s t h a t are designed t o b e i n t e r m i t t e n t ) .

good example i s a waste t a n k t h a t i s slowly f i l l e d w i t h waste s a l t over

a p e r i o d of about 1 y e a r , a f t e r which t h e s a l t i s h e l d up f o r a decay p e r i o d and f l u o r i n a t e d f o r uranium recovery.

I n a d d i t i o n , a number of

materials are accumulated o v e r t h e l i f e t i m e of a r e a c t o r .

As a r e s u l t ,

some materials must be removed by a d i s c a r d stream so t h a t t h e r e s i d e n c e time i s about one r e a c t o r l i f e t i m e i f the n u c l i d e s (e.g.,

l e a d ) are t o

be discarded. It i s a l s o d e s i r a b l e t o treat some n u c l i d e s (e.g.,

transuranium

i s o t o p e s ) i n a s t e a d y s t a t e c o n c e n t r a t i o n , even though s t e a d y s t a t e r e q u i r e s s e v e r a l r e a c t o r l i f e t i m e s t o achieve.

Although the code makes

a s t e a d y - s t a t e material b a l a n c e c a l c u l a t i o n , t h e convergence i s slowed down by t h i s k i n d of c a l c u l a t i o n , because the code r e q u i r e s t i m e t o p e r m i t t h e c o n c e n t r a t i o n s of t h i s material t o b u i l d up d u r i n g successive iterations. A steady state c a l c u l a t i o n â&#x201A;Źor processing p l a n t s with near t o t a l

r e c y c l e of any s p e c i e s r e q u i r e s u s e r c a u t i o n .

The e x i s t e n c e of any

material t h a t cannot b e removed from some r e g i o n o r group of r e g i o n s c a u s e s t h e system of e q u a t i o n s t o be s i n g u l a r , . s i n c e t h e c o n c e n t r a t i o n of t h i s material i n t h o s e r e g i o n s is undefined.

Iterations with the

r e a c t o r code do n o t a l t e r t h e c o n c e n t r a t i o n s of major s a l t components, and p r o v i s i o n i s made i n the p r o c e s s i n g p l a n t code f o r t h e c o n c e n t r a t i o n

of any n u c l i d e t o b e d e f i n e d by the i n p u t a t any p o i n t .

4.2

System o f U n i t s

I n t h e system o f u n i t s t h a t w a s u s e d , t h e code c a l c u l a t e d concent r a t i o n s i n moles p e r c u b i c c e n t i m e t e r by u s i n g flow r a t e s i n c u b i c c e n t i m e t e r s p e r second, volumes i n c u b i c c e n t i m e t e r s , e t c . ; however, t h i s i s n o t n e c e s s a r i l y implied by t h e e q u a t i o n s , s i n c e t h e y are j u s t

as v a l i d i n o t h e r systems of u n i t s (the n u c l e a r l i b r a r y u s e s seconds as t h e u n i t of time).

The most l o g i c a l a l t e r n a t e s e t of u n i t s i s t h e

d e s c r i p t i o n of volume i n moles, rates i n moles p e r second, e t c . , which r e s u l t s i n c o n c e n t r a t i o n s i n mole f r a c t i o n .

Some c a l c u l a t i o n s might

be changed by t h e u s e r who p r e f e r s t h i s s y s t e m of units.

For example,

t h e c a l c u l a t i o n of mole f r a c t i o n s i s redundant and might be r e p l a c e d by t h e c a l c u l a t i o n of c o n c e n t r a t i o n s i n moles p e r c u b i c c e n t i m e t e r . The g r e a t e s t a l t e r a t i o n r e q u i r e d i n such a change o f u n i t s i s t h e replacement of t h e o u t p u t headings.

By such l a b e l changes, i t would

b e p o s s i b l e t o t r e a t any system of e q u a t i o n s of t h i s form.

4.3

D e s c r i p t i o n of P a r t i c u l a r Items Using Mass T r a n s f e r C o e f f i c i e n t s

I n most s i m u l a t i o n s , t h e u s e of m a s s t r a n s f e r c o e f f i c i e n t s was limited t o gas-liquid

c o n t a c t s r e q u i r i n g one r e g i o n f o r t h e g a s phase

and one r e g i o n f o r t h e l i q u i d phase c o n t a i n i n g o n l y one o r two l i q u i d s . I t w a s assumed t h a t t h e n o b l e g a s c o n c e n t r a t i o n s w e r e small enough s o

t h a t no a p p r e c i a b l e e r r o r would occur by t r e a t i n g the g a s bubbles as i f they had t h e same c o n c e n t r a t i o n s as t h e b u l k g a s .

This i s n o t an essen-

t i a l assumption, however, s i n c e by u s i n g more r e g i o n s , the same case might be d e s c r i b e d as having more than one gas r e g i o n .

The b u l k gas

23 would be a s e p a r a t e r e g i o n from t h e gas b u b b l e s , and t h e gas bubbles i n s e p a r a t e l i q u i d s could e a s i l y be s e p a r a t e r e g i o n s .

I f t h e gas con-

c e n t r a t i o n changes as i t rises through t h e l i q u i d and i s n o t s m a l l r e l a t i v e t o i t s e q u i l i b r i u m c o n c e n t r a t i o n , t h e gas a t v a r i o u s levels i n t h e l i q u i d would be i n d i f f e r e n t r e g i o n s and would r e p r e s e n t a column. C a r e f u l c o n s i d e r a t i o n h a s a l s o been given t o s i m u l a t i o n of m a s s transfer-limited

t r a n s f e r rates as a replacement of e q u i l i b r i u m s t a g e s

i n a liquid-liquid

contactor.

For t u r b u l e n t flow when t r a n s f e r i s E m -

i t e d by eddy d i f f u s i v i t y , t h e o n l y d i f f i c u l t y arises i n s p e c i f i c a t i o n of the d i s t r i b u t i o n c o e f f i c i e n t s a t the i n t e r f a c e .

d e s c r i b e d by three r e g i o n s :

This case can be

the b u l k l i q u i d phase S , t h e b u l k l i q u i d

phase B , and t h e i n t e r f a c e c o n t a c t of b o t h phases.

The f l o w s between

t h e i n t e r f a c e r e g i o n and t h e b u l k l i q u i d r e g i o n are the r a t e s of eddy t r a n s p o r t i n each phase.

The product of eddy d i f f u s i v i t y and concentra-

t i o n d r i v i n g f o r c e i n each phase is I m p l i c i t l y o b t a i n e d i n two flow r a t e

terms f o r each phase i n t h e same manner d e s c r i b e d i n the s e c t i o n on m a s s transfer coefficients.

I n t h i s case, t h e d i s t r i b u t i o n c o e f f i c i e n t s can

s t i l l b e determined i t e r a t i v e l y by t h e same t e c h n i q u e used f o r e q u i l i b -

rium s t a g e s even though t h e d i s t r i b u t i o n c o e f f i c i e n t s are n o t expected t o b e t h e same.

4.4

U s e s Requiring Modifications

I t is p o s s i b l e t o c o n s i d e r f l o w s h e e t s i n v o l v i n g b a t c h p r o c e s s e s

t h a t might n o t b e r e p r e s e n t e d by either an e q u i l i b r i u m p r o c e s s o r a rate l i m i t e d p r o c e s s , because t h e amount of material t r a n s f e r r e d between t h e

phases w a s dependent on t h e c o n c e n t r a t i o n s of o t h e r elements as w e l l (e.g.,

oxide p r e c i p i t a t i o n ) .

The r a t e c o e f f i c i e n t s t h a t are used have

always remained c o n s t a n t , b u t t h i s i s n o t e s s e n t i a l t o t h e code s i n c e i t e r a t i o n i s r e q u i r e d t o converge o t h e r parameters i n t h e flowsheet. By u s i n g a r e a s o n a b l e estimate f o r p e r c e n t removal ( i . e . ,

rate c o n s t a n t s )

f o r v a r i o u s components, a set of c o n c e n t r a t i o n s would b e o b t a i n e d . Subroutine VOLUME would then b e used t o c a l c u l a t e t h e p r o p e r removal

rates on t h e b a s i s of t h e s e c o n c e n t r a t i o n s , and i t would modify the r a t e constants accordingly f o r t h e next i t e r a t i o n .

This system f o r t r e a t i n g

more g e n e r a l p r o c e s s i n g s t e p s should cause no g r e a t e r convergence probl e m than t h e i t e r a t i v e d e t e r m i n a t i o n of d i s t r i b u t i o n p a r a m e t e r s d e s c r i b e d

later. An a l t e r n a t i v e t o t h i s approach i s t o p r o v i d e c o n c e n t r a t i o n o r f e e d

rate l i n k s t o such a s u b r o u t i n e as i s done withMATADOR, o r even t o r e p l a c e MATADOR with a r o u t i n e s i m u l a t i n g some s e c t i o n o f the f l o w s h e e t . However, t h e most l i k e l y s u b s t i t u t i o n f o r MATADOR i s either a s u b r o u t i n e t h a t r e a d s and s t o r e s e n t e r i n g p r o c e s s i n g p l a n t c o n c e n t r a t i o n s o r one t h a t simulates a d i f f e r e n t r e a c t o r type.

I n t h i s l a s t c a s e , the r e a c t o r

and p r o c e s s i n g p l a n t need n o t b e l i n k e d d i r e c t l y and p r o c e s s i n g need n o t b e continuous ( i . e .

t h e r e can b e b a t c h replacements o f f u e l and a

decay p e r i o d ) ; t h e r e f o r e , t h e s t e a d y s t a t e performance of a system of r e a c t o r s and p r o c e s s i n g p l a n t s can b e o b t a i n e d .

5. 1.

REFERENCES

J . S. Watson, L. E. McNeese, and W. L. Carter, MSR Program Semiannu. P r o g r . Rep. Aug. 31, 1967, ORNL-4191, pp. 245-47.

M. J. B e l l and L. E. McNeese, Engineering Development S t u d i e s f o r Molten-Salt Breeder Reactor P r o c e s s i n g No. 1, ORNL/TM-3053

(November

1970) , pp. 38-48.

R. J. Ked1 and A. Houtzeel, Development of a Model f o r Computing 135Xe M i g r a t i o n i n t h e MSRE, ORNL-4069

H. F. Bauman e t a l . , ROD:

(June 1967).

A Nuclear and Fuel-Cycle A n a l y s i s Code f o r

C i r c u l a t i n g - F u e l R e a c t o r s , ORNL/TM-3359

(September 1971).

R. W. S c h a f t l e i n and T. W. F. R u s s e l l , "Two-Phase Reactor Design,"

W. L. Carter, ORNL, p e r s o n a l communication, June 1972.

M. J. B e l l , ORIGEN ORNL-4628

- The

(May 1973).

ORNL I s o t o p e Generation and D e p l e t i o n Code,

AF'PENDIXE S USER'S MANUAL

APPENDIX A:

DESCRIPTION OF SUBROUTINES USED

A d e s c r i p t i o n of each r o u t i n e used i n t h e program i s given i n t h e

approximate o r d e r of use.

S u f f i c i e n t i n f o r m a t i o n i s a v a i l a b l e t o permit

u s e of t h e program and some m o d i f i c a t i o n by u s e r s .

In p a r t i c u l a r , t h e

u s e r should be a b l e t o u t i l i z e the r e a c t o r s u b r o u t i n e s i n d e p e n d e n t l y of t h e p r o c e s s i n g p l a n t code by supplying any n e c e s s a r y i n f o r m a t i o n and

a main program which c a l l s MATADOR (with t h e BLOCK DATA r o u t i n e d e s c r i b e d i n t h e p r o c e s s i n g p l a n t code). S u b r o u t i n e MATADOR MATADOR d i r e c t s a l l the r e a c t o r c a l c u l a t i o n s .

It b e g i n s by r e a d i n g

t h e i n p u t d e f i n i n g the r e a c t o r and t h e v a r i a b l e s t h a t w i l l p r o v i d e an

i n i t i a l g u e s s f o r p r o c e s s p l a n t removal rates,

Through several calls

t o GRAPHT, i t sets up t h e c o e f f i c i e n t m a t r i x f o r n u c l e a r t r a n s i t i o n s

in t h e g r a p h i t e .

Whereas t h i s m a t r i x i s s t o r e d s e p a r a t e l y from the

corresponding matrix f o r t r a n s i t i o n s i n the s a l t , the p r o c e s s i n g p l a n t code can u s e t h e matrix f o r decay i n the s a l t , and the m a t r i x f o r g r a p h i t e may be changed between i t e r a t i o n s when the code i s used i t e r a t i v e l y w i t h ROD.

MATADOR b e g i n s by s e t t i n g up t h e c o n s t a n t v e c t o r and t h e d i a g o n a l ( t h e i n v e r s e of t h e d i a g o n a l e l e m e n t s i s c a l c u l a t e d t o save c a l c u l a t i o n a l

t i m e l a t e r on) f o r t h e c a l c u l a t i o n of t h e r e a c t o r s a l t c o n c e n t r a t i o n s . While t h e v a r i a b l e s X I N and DXIN are z e r o f o r t h e first c a l l t o MATADOR, t h e chemical removal r a t e o f each n u c l i d e i s assumed t o b e p r o p o r t i o n a l t o the reactor concentration. i n the d i a g o n a l element.

Hence, chemical p r o c e s s i n g i s s p e c i f i e d

Two a d d i t i o n a l o p t i o n s are a v a i l a b l e on subsequent c a l l s .

First,

i t may b e assumed t h a t t h e flow rate of a n u c l i d e i n t o t h e r e a c t o r (XIN)

i s independent of i t s c o n c e n t r a t i o n i n t h e r e a c t o r .

Second, i t may b e

assumed t h a t t h e f l o w r a t e of material i n t o t h e r e a c t o r i s a l i n e a r funct i o n of t h e r e a c t o r c o n c e n t r a t i o n .

I n t h i s c a s e , DXIN and t h e d e r i v a t i v e

of X I N w i t h r e s p e c t t o r e a c t o r c o n c e n t r a t i o n are nonzero.

I n considering

chemical p r o c e s s i n g , i t w a s n e c e s s a r y t o a l l o w n e g a t i v e e f f i c i e n c i e s t o a d e q u a t e l y t r e a t t h o s e n u c l i d e s produced by decay i n the p r o c e s s i n g p l a n t t h a t were removed p r i m a r i l y by n e u t r o n c a p t u r e s i n t h e r e a c t o r . Accordingly, care i s taken t o e n s u r e t h a t t h e d i a g o n a l elements do n o t approach zero.

A message i s p r i n t e d i f the d i a g o n a l element r e a c h e s some

predefined l i m i t i n g value. The program o b t a i n s a s o l u t i o n f o r t h e r e a c t o r s a l t w i t h a f i r s t

estimate b e i n g made f o r only t h e f i r s t c a l l t o MATADOR.

S o l u t i o n s are

t h e n o b t a i n e d f o r t h e n o b l e g a s e s and n o b l e metals that are i n c o n t a c t w i t h s a l t b o t h i n s i d e and o u t s i d e t h e r e a c t o r .

Noble g a s e s l e a v i n g t h e

holdup r e g i o n i n s i d e t h e r e a c t o r are s e n t t o t h e r e g i o n o u t s i d e t h e reactor.

The d i a g o n a l elements and t h e c o n s t a n t v e c t o r s a r e d e f i n e d s o

t h a t t h e c a l c u l a t i o n s p r o v i d e t h e holdup i n moles f o r n o b l e g a s e s and n o b l e metals, and the flow rate i n t o the s a l t i n moles p e r second f o r

a l l o t h e r materials.

The c a l c u l a t i o n a c t u a l l y assumes t h a t the r e t u r n i n g

n u c l i d e s are h e l d up f o r 1 s e c d u r i n g which t h e y may decay o r c a p t u r e neutrons.

I n t h e c a l c u l a t i o n s of t h e t r a n s f e r rates from t h e s e holdup

volumes t o t h e s a l t , t h e t h r e e systems of I e q u a t i o n s are weakly coupled and are assumed t o converge i n three p a s s e s .

T h i s may n o t be t r u e f o r

long holdup t i m e s i n these p h a s e s ; t h e r e f o r e , the v a l u e s are remembered

29 V

between c a l l s t o MATADOR s o t h a t each c a l l improves t h e v a l u e of t h e s e t r a n s f e r rates. Several o u t p u t parameters a r e c a l c u l a t e d b e f o r e c a l l i n g KEE, which

c o n t r o l s o u t p u t ; t h e s e are f i s s i o n product poisoning p e r f i s s i l e absorpt i o n Âś n u c l i d e p r o d u c t i o n rates, molar volume, uranium mole f r a c t i o n , and breeding r a t i o . is obtained.

I f t h e i n p u t v a r i a b l e KARD i s nonzero, punched o u t p u t

If KARD i s p o s i t i v e , t h e c o n c e n t r a t i o n s are i n a format f o r

6 i n p u t t o t h e CALDRON code; i f KARD i s n e g a t i v e , the c o n c e n t r a t i o n s are

i n a format f o r i n p u t t o ORIGEN.2

The ORIGEN i n p u t can a l s o b e prepared

by t h e c a l l i n g program s o t h a t a modified ORIGEN code may b e used as a second j o b s t e p .

S u b r o u t i n e AMATRX

The main f u n c t i o n of AMATRX i s t h e c o n s t r u c t i o n of the m a t r i x A , which c o n t a i n s decay and c a p t u r e rates f o r a l l t r a n s i t i o n s between i s o topes, except f i s s i o n .

The s u b r o u t i n e r e a d s the d a t a i n t h e format

d e s c r i b e d i n the s e c t i o n on i n p u t and writes a t a b l e summarizing the nuclear library.

N u c l i d e s are i d e n t i f i e d b y the v a l u e of 10,000 t i m e s

t h e atomic number p l u s 10 t i m e s t h e m o l e c u l a r weight ( p l u s 1 f o r e x c i t e d state).

It s t o r e s the i d e n t i f i c a t i o n of a l l decay d a u g h t e r s and c a p t u r e

p r o d u c t s i n a matrix NPROD w i t h t h e corresponding p r o d u c t i o n rates i n

COEFF.

I t a l s o s t o r e s t h e p a r e n t n u c l i d e i d e n t i f i c a t l o n , NUCL, t h e t o t a l

decay r a t e , DIS, and t h e c a p t u r e c r o s s s e c t i o n , TOCAP, as w e l l as h e a t g e n e r a t i o n r a t e s , the f r a c t i o n of heat which i s gamma energy, f i s s i o n product y i e l d s , e t c .

Thermal, r e s o n a n t , and f a s t n e u t r o n c r o s s s e c t i o n s

are s t o r e d so that the program can b e used i t e r a t i v e l y w i t h ROD by

allowing c o r r e c t i o n s based on t h e s p e c t r a l f a c t o r s determined by ROD t o be made t o t h e c r o s s s e c t i o n d a t a f o r t h e n e x t MATADOR c a l c u l a t i o n . The program then c o n s t r u c t s t h e v e c t o r A (C i n t h i s subroutine:, which c o n t a i n s t h e v a l u e of a l l nonzero p r o d u c t i o n r a t e s , and t h e corresponding v e c t o r LOC, which c o n t a i n s t h e o r d i n a l number of t h e p a r e n t n u c l i d e , assuming t h a t t h e daughter n u c l i d e s are i n t h e same o r d e r of t h e NUCLs.

These c o n s t a n t s are s t o r e d i n t h e o r d e r of p r o d u c t i o n by

decay, and by t h e r m a l , r e s o n a n t , o r f a s t n e u t r o n c a p t u r e s .

For each

n u c l i d e t h e r e are v a r i a b l e s KD, KTH, KRI, and NONO which s t o r e t h e cumulative number of terms f o r t h a t n u c l i d e w i t h t h e sum of a l l t h e NONOs b e i n g s t o r e d i n NON.

I n t h e s e v a r i a b l e s only members of a g i v e n S i m i l a r l y , t h e r e i s a set of

group produce n u c l i d e s i n t h a t group.

v e c t o r s i n d i c a t i n g t h e p r o d u c t i o n r a t e of f i s s i o n p r o d u c t s from t h e f i s s i o n of a c t i n i d e s . NOF

These v a r i a b l e s are denoted by F, LOF,

Kp,

and

. A v e c t o r NSTAR i s c o n s t r u c t e d s o t h a t f o r any NUCL w i t h atomic m a s s

NMASS, atomic number NATNO, and i s o m e r i c s t a t e (0 o r 1) NISOM:

NSTAR = NTEMP

+ NATNO*10

f o r p o s i t r o n e m i t t e r s , and NSTAR = NTEMP

- NATN0*10

f o r a l l o t h e r s , where NTEMP = NMASS*lOOOO

1000

+ NISOM.

A v e c t o r I O i s c o n s t r u c t e d which c o n t a i n s t h e o r d i n a l numbers of a l l

t h e n u c l i d e s i n d e c r e a s i n g o r d e r of NSTAR.

This i s i n decreasing order

of atomic m a s s w i t h t h e o r d i n a l number of e x c i t e d s t a t e n u c l i d e s appearing b e f o r e t h a t of t h e corresponding ground s t a t e n u c l i d e .

The sequence

I â&#x20AC;&#x2122;

i n c l u d e s p o s i t r o n emitters w i t h d e c r e a s i n g atomic numbers f o r a given atomic mass, followed by o t h e r n u c l i d e s w i t h i n c r e a s i n g atomic numbers. T h i s sequence i n c l u d e s a l l n u c l i d e s b e f o r e any of t h e i r decay d a u g h t e r s

as long as a l l decays r e p r e s e n t a l o s s of energy, mass, o r r e d u c t i o n i n E

+ MC2,

r a t h e r than a c a p t u r e of some kind.

T h i s sequence i s used

l a t e r i n t h e p r o c e s s i n g p l a n t code as t h e o r d e r of c a l c u l a t i o n . The v a r i a b l e s are dimensioned s o t h a t as many as 800 n u c l i d e s can b e i n c l u d e d , of which as many as 100 may b e a c t i n i d e s ; i n a d d i t i o n , t h e r e may b e as many as 1500 p r o d u c t i o n rates of n u c l i d e s from o t h e r n u c l i d e s by decay o r n e u t r o n a b s o r p t i o n .

The n u c l e a r l i b r a r y c o n t a i n s

739 n u c l i d e s , 99 a c t i n i d e s , and 1466 p r o d u c t i o n rate terms.

S u b r o u t i n e GRAPHT (DIS1, C A P 1 , DIS2,CAP2,COEFF,N,I,P2,VR,DEP,Dl,Pl,FLTJX2)

The s u b r o u t i n e GRAPHT c a l c u l a t e s rate c o e f f i c i e n t s f o r f i s s i o n product d e p o s i t i o n i n g r a p h i t e based on t h e d i f f u s i o n model d e s c r i b e d i n r e f . 2 , and t h e v a r i a b l e names are analogous: etc.

2 EN=n, E L = l , ENSQ=n ,

The c a l c u l a t i o n s are made t o determine FLUX2, which i s r e t u r n e d

t o b e i n s e r t e d i n a m a t r i x G , and i s analogous t o the m a t r i x A (described

w i t h AMATRX).

T h i s v a l u e r e p r e s e n t s the c o n t r i b u t i o n t o the concentra-

t i o n of s p e c i e s i from d i f f u s i o n i n t o g r a p h i t e of s p e c i e s j (A

described e a r l i e r ) .

ijâ&#x20AC;&#x2122;

The a d j u s t e d d i a g o n a l m a t r i x element for the p a r e n t

i s o t o p e (G ), t h e c o n t r i b u t i o n t o p o i s o n i n g by b o t h p a r e n t and daughter j i s o t o p e s i n t h e g r a p h i t e , and the d e p o s i t i o n rates of n o n v o l a t i l e daugh-

ters are a l s o c a l c u l a t e d . GRAPHT a l s o u s e s t h e v a r i a b l e s i n common b l o c k G R A T E that were r e a d by MATADOR:

AREA,VOL,PORTY,FILM,DTPFY,RADIUS, and SOLBTY.

These

v a r i a b l e s have been d e s c r i b e d i n t h e s e c t i o n on i n p u t .

The s u b r o u t i n e

r e q u i r e s a s u b r o u t i n e BESI f o r computing Bessel f u n c t i o n s . Subroutine BESI (X ,N ,B I ,IER) T h i s i s a l i b r a r y r o u t i n e which computes t h e Bessel f u n c t i o n , B I , of o r d e r N w i t h argument X , where N and X are g r e a t e r than o r e q u a l t o I E R is used as an e r r o r i n d i c a t i o n .

zero.

IER

meaning

no e r r o r

N is negative

X is negative

underflow, BI.LT.l.E-69,BI

overflow, X.GT.170 where X.GT.N

set t o 0.0

Only Bessel f u n c t i o n s of o r d e r s 0 and 1 are r e q u i r e d by G W H T . Subroutine CHEMPL

The v a l u e of t h e r e c i p r o c a l o f the removal time f o r the group of

which t h a t n u c l i d e i s a member i s s t o r e d i n the v a r i a b l e PR(1) ( p r o c e s s i n g r a t e ) f o r each n u c l i d e .

On t h e f i r s t c a l l , the r o u t i n e u s e s the group

removal t i m e s (NTIME) t h a t are used f o r o u t p u t purposes and the e f f i c i e n c i e s assumed f o r each element t o c a l c u l a t e a removal time f o r each element i n t h e u n i t s used f o r t h a t group of elements. f o r output.

This is written i n a t a b l e

I n a d d i t i o n , on t h e f i r s t c a l l t h e program adds t o the

m a t r i x elements f o r p r o d u c t i o n of uranium from p r o t a c t i n i u m an amount which assumes t h a t a l l p r o t a c t i n i u m removed by chemical p r o c e s s i n g decays t o uranium and i s r e t u r n e d t o t h e r e a c t o r .

A c a l l t o another e n t r y point

33 V

(ENTRY REPAIR) c a u s e s t h e s e amounts t o b e s u b t r a c t e d from t h e proper

m a t r i x e l e m e n t s , t h u s assuming t h a t t h e l i n k t o t h e p r o c e s s i n g p l a n t r o u t i n e s t a k e s t h i s i n t o account. S u b r o u t i n e GAUSS (XEQL ,C ,D,*) GAUSS s o l v e s t h e matrix e q u a t i o n :

A(XEQL) = C

p\,

where A i s t h e c o e f f i c i e n t matrix, and r e c i p r o c a l s of t h e d i a g o n a l elements are given by D.

A nonstandard r e t u r n i s made i f t h e system does

n o t converge w i t h i n t h e maximum a l l o w a b l e number of i t e r a t i o n s .

The

groups of terms i n c l u d e d i n t h e c o e f f i c i e n t matrix are determined by t h e v a l u e of t h e l o g i c a l v a r i a b l e s REGION, and REG2. Subroutine KEE

S u b r o u t i n e KEE e n s u r e s t h a t s u b r o u t i n e RESULT (described n e x t ) i s c a l l e d i f t h i s is t h e l a s t call t o MATADOR as i n d i c a t e d by t h e l o g i c a l v a r i a b l e ILLOG.

Subroutine KEE p r i n t s t h e number of c a l l s t o MATADOR

and a convergence message, and c a l l s RESULT a t s p e c i f i e d i n t e r v a l s .

S u b r o u t i n e RESULT (XEQL)

RESULT p r i n t s o u t p u t t a b l e s f o r a given set of r e a c t o r concentrat i o n s (XEQL).

It f i r s t c a l c u l a t e s t h e number of moles of material i n t h e

stream r e t u r n i n g t o t h e r e a c t o r f o r u s e i n t h e c a l c u l a t i o n of mole f r a c t i o n f o r t h a t stream. W

v a r i a b l e s such as:

It t h e n i n i t i a l i z e s o r c a l c u l a t e s o t h e r important

m a s s of materials l o s t due t o f i s s i o n ,

F I SSL

= the

FISSN

= a b s o r p t i o n r a t e by t h e f i v e f i s s i o n a b l e i s o t o p e s ,

FISSA

= a b s o r p t i o n r a t e by f i s s i l e i s o t o p e s ,

DMOLAR

= molar d e n s i t y ,

TOCAP(1GAS) = t h e a d j u s t e d c r o s s s e c t i o n f o r n o b l e g a s e s t h a t r e f l e c t s t h e number of a b s o r p t i o n s of n o b l e g a s e s i n graphite. The program c a l c u l a t e s t h e gamma h e a t rate i n t h e s a l t , t h e absorpt i o n rate i n t h e s a l t normalized t o a b s o r p t i o n s p e r f i s s i o n , t h e removal

r a t e due t o chemical p r o c e s s i n g , and t h e c o n t r i b u t i o n t o r a d i o a c t i v i t y i n t h e s a l t f o r each of t h e t h r e e groups of n u c l i d e s ( l i g h t e l e m e n t s , a c t i n i d e s , and f i s s i o n p r o d u c t s ) .

A series of c a l l s t o s u b r o u t i n e SORT

i s used t o i d e n t i f y t h e 2 5 most important materials i n each c a t e g o r y . C a l c u l a t i o n s f o r t h e f i s s i o n p r o d u c t s are somewhat complicated by t h e c o n t r i b u t i o n of n u c l i d e s i n t h e c i r c u l a t i n g bubbles and by t h e c o n t r i b u t i o n of n u c l i d e s p l a t e d o n t o t h e r e a c t o r s u r f a c e s .

Once t h e s e are p r i n t e d ,

t h e program p r i n t s t h e t o t a l s f o r removal of f i s s i o n p r o d u c t s and a c t i n i d e s , t h e burnup r a t e of thorium, and a c o r r e c t i o n f a c t o r based on t h e n u c l e a r t r a n s i t i o n s t o nuclides not l i s t e d i n the l i b r a r y .

A correction factor

n o t considered i s t h e amount by which t h e average m a s s y i e l d from f i s s i o n ,

as g i v e n i n t h e l i b r a r y , f a i l s t o match t h e m a s s of t h e f i s s i o n a b l e n u c l i d e less t h e average number of n e u t r o n s e m i t t e d .

Additional important v a r i a b l e s

i n t h i s s u b r o u t i n e are : COMPNG = composition of n o b l e g a s e s ,

COMPNM

= compositions of n o b l e

me ta ls,

HEATNM = h e a t g e n e r a t i o n r a t e s of n o b l e metals,

COMPBI = composition of materials e x t r a c t e d i n t o bismuth, COMPRE = composition of rare e a r t h s ,

COMPF2 = compositions of materials removed from f l u o r i n a t o r s , primarily t h e halogens, COMPLB = compositions of materials removed i n group 6 by chemical

processing, SRATE = sum of t h e removal r a t e f o r each n u c l i d e group, SHEAT = sum of t h e h e a t g e n e r a t i o n rates i n each group, and

SCAPT = sum of t h e a b s o r p t i o n rates i n each group.

MAIN Program

The main program c o n t r o l s t h e p r o c e s s i n g p l a n t c a l c u l a t i o n s , and b e g i n s by c a l l i n g MATADOR f o r s e t t i n g up t h e m a t r i x f o r decay c h a i n s . It t h e n r e a d s t h e i n p u t d e s c r i b i n g t h e f l o w s h e e t and p r i n t s t h e t a b l e s

of i n p u t d a t a .

Region names are compared w i t h stream o r i g i n and des-

t i n a t i o n s t o c o n s t r u c t v e c t o r s which d e s c r i b e t h e s e streams by t h e o r d i n a l numbers of t h e r e g i o n names,used. f r a c t i o n a l flows are determined.

I n a d d i t i o n , t o t a l flows and

A l l streams with a d e s t i n a t i o n n o t i n

t h e l i s t of r e g i o n names are assumed t o be d i s c a r d streams and are added t o t h e l o s s rates.

The program c a l l s s u b r o u t i n e EQKN t o d e f i n e t h e

e q u i l i b r i u m c o n s t a n t s t o be used. The program t h e n alternates c a l l s t o MATADOR w i t h c a l c u l a t i o n s of processing plant concentrations.

P r o c e s s i n g plant c o n c e n t r a t i o n s are

c a l c u l a t e d f o r one n u c l i d e a t a t i m e i n t h e o r d e r d e f i n e d by I O t o e n s u r e t h a t decay p r o d u c t s f o l l o w t h e i r p r e c u r s o r s .

The program d e f i n e s

a c o e f f i c i e n t matrix and two c o n s t a n t v e c t o r s f o r each n u c l i d e b e f o r e

c a l l i n g a s u b r o u t i n e MATQD t o s o l v e t h e two s e t s of e q u a t i o n s r e p r e s e n t e d . The f i r s t c o n s t a n t v e c t o r d e f i n e s t h e p r o d u c t i o n rates of t h e n u c l i d e and r e s u l t s i n t h e l i s t of c o n c e n t r a t i o n s .

T h e second v e c t o r has i t s

only nonzero v a l u e corresponding t o t h e r e a c t o r , and i t r e s u l t s i n t h e s o l u t i o n of t h e c o n c e n t r a t i o n s f o r t h e c a s e of no p r o d u c t i o n by decay i n t h e p r o c e s s i n g p l a n t ; i f i n s t r u c t e d t o do s o , i t determines t h e i n f l u e n c e of r e a c t o r c o n c e n t r a t i o n on the e f f l u e n t from t h e p r o c e s s i n g plant. I f t h e i n p u t i n s t r u c t i o n s s p e c i f y averaging between i t e r a t i o n s , t h e program averages c o n c e n t r a t i o n s t o and from t h e r e a c t o r , and a v e r a g e s removal times w i t h t h e i r p r e v i o u s v a l u e s .

It a l s o checks f o r conver-

gence (perhaps an ordered l i s t of t h e r e a c t o r i n l e t c o n c e n t r a t i o n s i n d e c r e a s i n g o r d e r of t h e i r r e l a t i v e change i n t h e l a s t i t e r a t i o n ) and p r i n t s t h e f i r s t 50 i n t h i s l i s t .

VOLUME i s c a l l e d f o r p o s s i b l e modifi-

c a t i o n of t h e flowsheet p a r a m e t e r s , and a l o g i c a l v e c t o r i s d e f i n e d t h a t i d e n t i f i e s t h e n u c l i d e s that have converged; t h e r e f o r e , t h e y need o n l y b e considered on every t e n t h i t e r a t i o n . A f t e r t h e c a l c u l a t i o n s have converged, o r t h e program r e a c h e s t h e allowed t i m e l i m i t o r number of i t e r a t i o n s , a deck of punched c a r d s is prepared.

I f I 2 i s g r e a t e r t h a n z e r o , t h e deck i n c l u d e s r e a c t o r e f f l u e n t

c o n c e n t r a t i o n s and removal e f f i c i e n c i e s f o r a l l t h e n u c l i d e s .

I f I6 is

g r e a t e r than z e r o , much of t h e d e s c r i p t i o n of t h e p r o c e s s i n g p l a n t i s included.

The program then calls OUT0 and s t o p s .

BLOCK d a t a .

A b l o c k d a t a s u b r o u t i n e i s used t o i n i t i a l i z e t h e

100-element v a r i a b l e ELE t o t h e element symbols, and the v a r i a b l e STA(1) and STA(2) t o b l a n k and

"MI'.

Subroutine EQKN

EQKN r e a d s d a t a f o r d i s t r i b u t i o n c o n s t a n t s and ass-gns v a l u e s t o

t h e d i s t r i b u t i o n c o e f f i c i e n t m a t r i x , EQK.

The d a t a are s e l e c t e d f o r

c h a r a c t e r i z i n g a r e g i o n by matching an i n p u t v a r i a b l e (NS) i n t h e d a t a w i t h t h e i n p u t v a r i a b l e (NSTR) corresponding t o t h e r e g i o n .

For region

REGION(N), t h e d i s t r i b u t i o n c o e f f i c i e n t f o r t h e element w i t h atomic number NZ i s EQK((N-l)*lOO+NZ).

For NS = 1 o r NS = 2 t h e v a l u e of NSTR

i s used t o choose between two temperatures.

I f NS = NSTR(N),

t h e calcu-

l a t i o n assumes a temperature of 6 4 0 O C ; i f NS+20 = NSTRCN), t h e c a l c u l a t i o n assumes a temperature of 550째C.

Sufficient data is stored i n variables

IAE, A I E , AKE, and BKE t o later a l l o w a d i f f e r e n t c a l c u l a t i o n f o r t h e s e d i s t r i b u t i o n c o e f f i c i e n t s i n VOLUME.

S u b r o u t i n e VOLUME ("LEFT)

On t h e f i r s t c a l l t o VOLUME, t h e i n p u t v a r i a b l e s are r e a d , each phase i s a s s i g n e d a s t a r t i n g molar d e n s i t y , and each r e g i o n i s a s s i g n e d

a r a t i o of molar d e n s i t i e s f o r u s e i n c o n v e r t i n g d i s t r i b u t i o n c o n s t a n t s from r a t i o s of mole f r a c t i o n t o r a t i o s of c o n c e n t r a t i o n s .

E s t i m a t e s of

molar d e n s i t y are found i n t h e v a l u e s of WEST and W E S T f o r f i r s t and second p h a s e s , r e s p e c t i v e l y .

The 1 6 v a l u e s i n each v e c t o r correspond t o

t h e v a l u e s of t h e two hexadecimal d i g i t s of NC which i d e n t i f y t h e phases present. On subsequent c a l l s , VOLUME b e g i n s by c a l c u l a t i n g new v a l u e s of

X L I B f o r t h o s e r e g i o n s w i t h NV.LT.0.

The e n t e r i n g e q u i v a l e n t d e n s i t y

f o r a given r e g i o n i s determined by u s i n g t h e t a b l e s of v a l e n c e s , and

f o r specifying the equivalent density i n t h a t region i f the value s u p p l i e d on i n p u t i s less t h a n 0.

The e q u a t i o n s f o r c o n c e n t r a t i o n s

i n t h e r e g i o n are t h e n solved f o r each new i n t e r m e d i a t e lithium d i s t r i b u t i o n X L I , w i t h t h e e q u i v a l e n t d e n s i t y and t h e d e r i v a t i v e o f e q u i v a l e n t d e n s i t y w i t h r e s p e c t t o XLI being determined f o r each s o l u t i o n .

Each

new X L I v a l u e i s t h e n determined by Newton's method, b u t w i t h X L I confined t o c o n t i n u a l l y r e a d j u s t i n g narrowing limits based on t h e s i g n of t h e d i f f e r e n c e of e q u i v a l e n t d e n s i t y and t h e r e f e r e n c e v a l u e .

A logical variable

DECIDE i s d e f i n e d t o i d e n t i f y a l l n u c l i d e s t h a t have a s i g n i f i c a n t i n f l u e n c e

on t h e d e r i v a t i v e of e q u i v a l e n t b a l a n c e w i t h r e s p e c t t o XLI.

NLEFT i s the

number of r e g i o n s r e q u i r i n g more than one i t e r a t i o n . The converged v a l u e s of XLI are s t o r e d i n X L I B s o t h a t new d i s t r i b u t i o n c o e f f i c i e n t s can be determined l a t e r , j u s t b e f o r e r e t u r n i n g t o t h e main program.

Before t h i s c a l c u l a t i o n i s done, however, t h e molar volume

i s c a l c u l a t e d f o r a l l p h a s e s i n d i c a t e d by t h e f i r s t d i g i t of NC.

This

i s used t o r e d e f i n e t h e v a l u e s f o r molar d e n s i t y , t o t a l flow rate, and r a t i o s of molar d e n s i t i e s f o r u s e as a conversion f a c t o r f o r t h e d i s t r i bu t i o n coef f i c i e n t s

T h i s s u b r o u t i n e i s used t o change f l o w s h e e t p a r a m e t e r s between iterations.

well.

It could e a s i l y be modified t o a d j u s t o t h e r parameters as

The most p r o b a b l e a d j u s t a b l e parameter i s t h e rate c o e f f i c i e n t

t a b l e t h a t would be a d j u s t e d t o match some a r b i t r a r y f u n c t i o n of processing plant concentrations.

T h i s i s t h e method c o n s i d e r e d f o r

s i m u l a t i n g t h e oxide p r e c i p i t a t i o n flowsheet that involved n o n l i n e a r -

i t i e s , n o n e q u i l i b r i u m c o n t a c t s , and b a t c h o p e r a t i o n s .

Subroutine MATQD (A,X,NR,NV,DET ,NA,NX)

MATQD s o l v e s a system of l i n e a r a l g e b r a i c e q u a t i o n s i n double

p r e c i s i o n , w i t h c o e f f i c i e n t m a t r i x A and c o n s t a n t v e c t o r X, and r e t u r n s w i t h t h e s o l u t i o n v e c t o r i n X.

Any number, NV, of systems of e q u a t i o n s

w i t h t h e same c o e f f i c i e n t matrix may be s o l v e d by i n c l u d i n g NV c o n s t a n t v e c t o r s , e a c h of which occupies t h e f i r s t NR p o s i t i o n i n c o n s e c u t i v e segments i n X of l e n g t h NX; t h u s , A

= t h e c o e f f i c i e n t matrix, where t h e element i n row I and

column J i s element number (J-l)*NA+I. X

= s o l u t i o n v e c t o r and c o n s t a n t v e c t o r .

The p o s i t i o n r e p r e s e n t e d

by v a r i a b l e I i n t h e s o l u t i o n s e t K i s (K-l)*NX+I.

= number of unknowns.

= number of s o l u t i o n s r e q u i r e d w i t h t h e

m a t r i x A.

DET = r e t u r n s w i t h v a l u e 0.0 f o r a s i n g u l a r m a t r i x and a v a l u e 1.0

f o r a n o n s i n g u l a r matrix.

O r i g i n a l l y , DET w a s t h e v a l u e of

t h e determinant of A. NA

= number of elements i n A allowed f o r each column.

= number of elements i n X allowed for each set of e q u a t i o n s .

V a r i a b l e s A, X, and DET are double p r e c i s i o n . MATQD w a s o r i g i n a l l y o b t a i n e d from t h e ORNL computer l i b r a r y ; however, t h e s o l u t i o n h e r e i n v o l v e s a s p a r s e m a t r i x .

For t h i s r e a s o n ,

m o d i f i c a t i o n s w e r e made t o have t h e s u b r o u t i n e check f o r z e r o s b e f o r e performing m u l t i p l i c a t i o n s and d i v i s i o n s i n t h e c o e f f i c i e n t m a t r i x .

v e c t o r ISTAR was d e f i n e d t o remember t h e row numbers of up t o 50 rows, w i t h nonzero elements below t h e p i v o t element t o b e e l i m i n a t e d i n a

given r e d u c t i o n s t e p .

A f t e r m o d i f i c a t i o n , the r o u t i n e o b t a i n e d the

solution i n one-fifth the t i m e required previously.

T h i s modified ver-

s i o n h a s been used t o r e p l a c e t h e l i b r a r y v e r s i o n i n one o t h e r i n s t a n c e , and i t achieved a s o l u t i o n i n one-third t h e t i m e r e q u i r e d p r e v i o u s l y .

S u b r o u t i n e OUTO

OUTO s u p p l i e s i n p u t f o r t h e modified ORIGEN7 code used as a second

j o b s t e p and p r i n t s a l l o u t p u t t a b l e s t h a t supply c o n c e n t r a t i o n s o r h e a t

g e n e r a t i o n rates.

I t r e q u i r e s t h e f u n c t i o n NOAH, d e s c r i b e d p r e v i o u s l y ,

f o r producing alphameric names from n u c l i d e i d e n t i f i c a t i o n s .

It a l s o

c a l l s t h e s u b r o u t i n e OUTL.

S u b r o u t i n e OUTL (REG, RAY RB, XL, YL, NR)

OUTL s e a r c h e s through t h e l o s s rates and p r i n t s a summary of t h e

l o s s r a t e s from t h e p r o c e s s i n g p l a n t , where

REG

= l i s t o f r e g i o n names,

= l i s t of f i r s t - p h a s e

= l i s t of second-phase

= f i r s t - p h a s e l o s s rates,

= second-phase

= number of r e g i o n s .

names, names,

l o s s rates, and

Miscellaneous S h o r t Routines

Subroutine SORT (X,LABEL ,Y ,NAME ,NX,NY) SORT makes one p a s s through t h e v e c t o r , Y , and i n s e r t s t h e values of Y and NAME i n t h e v e c t o r s X and LABEL s o t h a t t h e X v a l u e s are i n

41 decreasing order.

X and LABEL have dimension NX i n s u b r o u t i n e SORT,

w h i l e Y and NAME have dimension NY.

S u b r o u t i n e ZERO(A,B,N) ZERO z e r o e s the space between a d d r e s s A and B i n c l u s i v e i n u n i t s

of N b y t e s .

S u b r o u t i n e HALF(A. I)

-1

HALF computes t h e decay c o n s t a n t , A , i n u n i t s of s e c

from the

h a l f - l i f e A i n u n i t s denoted by I , where I corresponds t o IU i n t h e nuclear library.

Function NOAH (NUCLI) T h i s r o u t i n e c o n s t r u c t s a three-word alphameric symbol f o r an i s o t o p e from i t s s i x - d i g i t i d e n t i f y i n g number, NUCLI.

The t h r e e words

c o n s i s t of t h e symbol f o r t h e chemical element, t h e atomic weight, and e i t h e r a b l a n k o r an ”M” t o d e s i g n a t e a ground s t a t e o r m e t a s t a b l e s t a t e . These symbols are used only when p r i n t i n g o u t p u t t a b l e s .

APPENDIX B:

INPUT

The i n p u t d e s c r i p t i o n i s arranged by s u b r o u t i n e names i n the o r d e r The i n p u t d e s c r i p t i o n i s f u r t h e r d i v i d e d so

i n which t h e y are c a l l e d .

t h a t each t y p e of i n p u t card can b e i d e n t i f i e d .

The argument l i s t and

t h e format are given f o r each r e a d s t a t e m e n t .

Nuclear L i b r a r y (AMATRX)

NDT:

(-110) used t o determine format f o r n u c l e a r l i b r a r y .

c a r d 1:

80 c h a r a c t e r t i t l e ; alphameric format

card 2:

ERR, NMO,

NDAY, NYR, NGO

FORMAT (F10.5 ,412) ERR = number below which c o n s t a n t s (decay c o n s t a n t s ,

e t c . ) w i l l b e assumed t o b e z e r o NMO, NDAY, NYR = d a t e , month, day, y e a r used as heading NGO

no l o n g e r used.

c a r d 3 : NSORS (I), I = l,5 FORMAT (5110) The s i x - d i g i t

mater ia1s

i d e n t i f y i n g numbers f o r t h e f i v e f i s s i o n a b l e

233u

235tT 232Th, Y

238U,

and 239Pu.

These must

be i n o r d e r , because t h e y r e f e r t o columns of d a t a on f i s s i o n product y i e l d s . The s i x - d i g i t

i d e n t i f y i n g numbers are made up s o t h a t t h e h i g h e s t

o r d e r d i g i t s g i v e t h e atomic number, t h e n e x t t h r e e d i g i t s g i v e t h e atomic m a s s , and t h e lowest o r d e r d i g i t i s 0 f o r ground s t a t e and 1 f o r e x c i t e d

state.

This i s t h e same system used by t h e ORIGEN7 code.

The n e x t c a r d s

43 d e s c r i b e t h e p r o p e r t i e s of each n u c l i d e i n the n u c l e a r l i b r a r y .

If t h e

p r e v i o u s l y r e a d v a r i a b l e , NDT i s nonzero, t h e l i b r a r y i s read from u n i t 7 i n t h e f o r m a t s g i v e n i n r e f . 7. disc files.

U n i t 7 h a s u s u a l l y been a series of

For NDT=O t h e l i b r a r y i s r e a d on u n i t 50 i n t h e format and

o r d e r given h e r e .

L i g h t Elements

NUCL(1)

, DLAM,TU,FBI,FP,FPI,FT,FA,SIGTH,l?"Gl

,FNA,FNP,RITH,FINA,FINP

SIGMEVyFN2N1,FFNA,FFNP,Q,FG FORMAT (I6 ,F5.3 ,11,5F5.3 ,E5.2,3F3.3 ,E5.2 JF3.3 ,E5.2,3'P3.3 ,F4 3 ,F3 3 ,F6.3) Ended by NUCL ( I ) = O A c ti n i d e s NUCL (I) ,DLAM ,IU ,FBI,FP ,'FPI,FT ,FA,SIGNA ,RING,FNGl ,S IGF ,RIF ,SIG'FF ,SIGN2N ,

FN2N1 ,Q ,FG,SIGN3N ,FSF

FORMAT(I6,F5.3,11,5F3.3,2E5.2,F3.3,4E5.2,F3.3,F4.4,F3.3,2E5.2) Ended by NUCL(I)=O

SIGN3N, and FSF are n o t used. 'Fission P r o d u c t s

Ended by NUCL(I)=O

*These v a r i a b l e

names are n o t the names of program v a r i a b l e s but

were chosen t o conform t o the names used i n and d e f i n e d by ref. 7.

MATADOR I n p u t

T i t l e c a r d ; 80 c h a r a c t e r s , alphameric format.

RUX, POWER, FLOW1, THERM, RES, FAST, FPABS

FORMAT (8F10.5 ) FLUX

= nominal--flux,

-2

-1 sec

POWER = power, MW(t) F L O W 1 = f e e d r a t e , e q u i v a l e n t p e r second THERM = thermal spectrum f a c t o r

RES

= resonance spectrum f a c t o r

FAST

f a s t spectrum f a c t o r

FPAES = r e f e r e n c e f i s s i o n product a b s o r p t i o n . C.

EPS, ERR, MAX, U R D FORMAT (2F10.3 ,2 I 5 )

EPS

= e r r o r c r i t e r i o n i n Gauss-Seidel

solution

ERR

= number l e s s t h a n which c o n c e n t r a t i o n s w i l l b e considered

zero MAX

maximum number of i t e r a t i o n s allowed f o r s o l u t i o n

KARD = s i g n a l f o r punched o u t p u t , i f no punched c a r d s from

MATADOR. D.

AREA, VOL, RADIUS, PORTY, FILM, DIFFY, SOLBTY, VRATIO FORMAT (8E10.3) AREA

= g r a p h i t e area,

VOL

= s a l t volume,

RADIUS = g r a p h i t e rod r a d i u s , cm

PORTY

= g r a p h i t e p o r o s i t y , cc-void/cc

FILM

= m a s s t r a n s f e r c o e f f i c i e n t f o r krypton,

cm/sec

= d i f f u s i v i t y of krypton i n p o r e s , cm /sec

DIFFY

SOLBTY = s o l u b i l i t y of krypton i n f u e l s a l t (mole/cc of l i q u i d ) /

(mole/cc of g a s )

VRATIO = r a t i o of g r a p h i t e volume t o s a l t volume i n c o r e ; i f AREA=O n e x t c a r d i s t y p e G. E.

IGAS, IDAU, IENT, 1 3 , I3DEP, NEXT

FORMAT ( 4X,16 ,4X,16,IS ,4X,16,2I5) IGAS

= gas i d e n t i f i e r

IDAU

i d e n t i f i c a t i o n of daughter

IENT

0 i f daughter d e p o s i t s

1 i f daughter i s v o l a t i l e

= i d e n t i f i c a t i o n of granddaughter formed

from v o l a t i l e

daughter I3DEP = same as IENT e x c e p t t h a t i t r e f e r s t o I3 NEXT

= number used t o c o n t r o l program

> 0 r e t u r n t o next type E card = 0 r e a d t y p e G card

< 0 r e a d type F c a r d followed by one of type E. The f i r s t s e t r e f e r s t o d a u g h t e r s of k r y p t o n , t h e n e x t set a f t e r t h e type F c a r d r e f e r s t o d a u g h t e r s of xenon.

PILM,DIJ?E'Y,SOLBTY FORMAT (3E12.5)

The v a r i a b l e s are d e f i n e d i n t h e same way as t h o s e of c a r d type D. t h i s c a r d , t h e n e x t c a r d r e a d i s of t y p e E.

After

46 G.

INPUT(1) ,X(I) ,I=1,4 FORMAT(4(15,F10.3)) INPUT

= six-digit

i d e n t i f i e r of n u c l i d e

= composition i n atom f r a c t i o n o r mole f r a c t i o n .

The materials f e d t o t h e r e a c t o r are 'Li, The molar f e e d rate i s FLOW1

* X(1)

'Be,

232Th, and "F.

i n g-atom/sec.

TIME (N) ,N=l,10 FORMAT (10E8.1) TIME(N)

= t h e removal time f o r group

N of elements.

I. NP(1) ,I=1,100 FORMAT (40 (12)) NP(1) = t h e group number f o r element w i t h atomic number I. J.

NZ(1) ,EFF(I) ,I=1,8 FORMAT(8(13,F7.4)) EFF

= t h e removal e f f i c i e n c y of t h e element w i t h atomic number

NZ.

Only t h o s e elements w i t h a removal e f f i c i e n c y d i f f e r e n t from 1.0 need b e specified.

As many c a r d s as n e c e s s a r y may b e used w i t h i n p u t of EFFs,

s t o p p i n g when NZ-0 i s encountered. K.

THETA

= six values.

FORMAT (8F10.3) THETA(1)

= holdup time of group 1 elements (noble g a s e s ) i n t h e

c i r c u l a t ing g a s bubbles

THETA(2)

= holdup of group

2 elements (noble m e t a l s ) d e p o s i t e d

i n t h e r e a c t o r core.

THETA(3) = holdup of group 3 elements (seminoble metals) d e p o s i t e d i n t h e r e a c t o r core.

-C.

THETA(4) = holdup of group 1 elements i n c o n t a c t w i t h s a l t o u t s i d e t h e f l u x of t h e r e a c t o r .

The gas i s assumed

t o be t h e e f f l u e n t of g a s e s from t h e r e a c t o r . THETA(5),THETA(6) = holdup time of group 2 and 3 elements, respectively, i n contact with salt outside the reactor. L.

NTINE(1) ,PUNIT(I) ,I=1,10 FORMAT(lO(I.4 ,A4))

NTIME(1) = t h e removal t i m e of group I elements expressed i n u n i t s of PUNIT(1); t h e s e are used only f o r p r i n t o u t purposes when going through MATADOR f o r t h e f i r s t t i m e .

NZ(I),EFF(I),I=l,8 FORMAT (8 (13, F7.4) )

The v a r i a b l e s are d m y v a r i a b l e s w i t h no r e l a t i o n t o t h e v a r i a b l e s r e a d as c a r d t y p e J .

Here NZ i s an atomic number as b e f o r e , b u t EFF i s

a f r a c t i o n of t h e element of group 2 o r 3 which i s p l a t e d o u t i n t h e The remaining m a t e r i a l i s assumed t o b e d e p o s i t e d o u t s i d e t h e

reactor.

reactor flux.

A s many c a r d s are r e a d as n e c e s s a r y u n t i l NZ=O i s encountered.

MAIN i n p u t

The main program p r i m a r i l y r e a d s i n p u t d e s c r i b i n g t h e f l o w s h e e t and v a r i a b l e s which c o n t r o l e x e c u t i o n and o u t p u t .

The c a r d s t h a t f o l l o w a r e

r e a d from u n i t 2:

11,12,13,14,15,16,17,18,19,110,NWASTE,112,113,11~,115 FORMAT (1615)

Explanation of v a r i a b l e s :

I f I1.GT.O flowsheet i n p u t c o n c e n t r a t i o n s and removal e f f i c i e n c i e s are i n p u t from p r e v i o u s c a s e s w i t h 12.GT.0.

If 12.GT.0 punch o u t p u t t o be r e a d i f I1.GT.O

P r e d i c t e d number of i t e r a t i o n s ; maximum number of i t e r a t i o n s when no t i m e l i m i t i s used.

Not needed

If 16.GT.O flowsheet i n f o r m a t i o n i s punched f o r l a t e r i n p u t when I8.GT.O.

Not needed

If 18.GT.0 flowsheet i n f o r m a t i o n i s r e a d from c a r d s punched e a r l i e r .

No averaging i s done on c o n c e n t r a t i o n s u n t i l 19 i t e r a t i o n s a r e complete.

I10

I f IIO.GT.O averaging i s n o t done on c o n c e n t r a t i o n s between i t e r a t i o n s .

WASTE

Number of w a s t e streams

I12

I f t h e number of i t e r a t i o n s i s less than t h i s , n u c l i d e s

are n o t excluded because t h e y do n o t a f f e c t D values. Li

I13

I13 i t e r a t i o n s are made a t end i n which n u c l i d e s do n o t a f f e c t DLi v a l u e s , and are n o t excluded.

I14

I f 114.GT.0, t h e program s u p p l i e s MATADOR w i t h a d e r i v a t i v e of r e a c t o r i n l e t c o n c e n t r a t i o n w i t h r e s p e c t t o reactor o u t l e t concentration,

I15

I f 115.GT.0, t h e program s t a r t s o u t p u t s e c t i o n a f t e r

I15 minutes of c a l c u l a t i o n .

EPS, ERR, MAX

FORMAT (2F10.3, 15) Explanation of v a r i a b l e s :

EPS

Convergence c r i t e r i o n d i v i d e d by 10 ( t y p i c a l v a l u e ) .

ERR

Number below which c o n c e n t r a t i o n s are set t o 0.0.

MAX

Not used.

WTDX FORMAT (F10.3) WTDX = t h e weighting f a c t o r g i v e n t o DXIN.

NREG, N I N X , N I N Y , NINP, NRATE, KRATE, SRATE

FORMAT (1615) E x p l a n a t i o n of v a r i a b l e s : NREG

Number of r e g i o n s .

NINX

Number of f i r s t - p h a s e flowing streams.

NINY

Number of second-phase

NINP

Number of f e e d streams i n p r o c e s s i n g p l a n t .

NRATE

flowing streams.

Number of r a t e streams u s i n g a scale f a c t o r and a t a b l e number.

KRATE

Number of r a t e streams d e s c r i b e d by parameters of g a s - l i q u i d c o n t a c t f o r g a s bubbled i n t o tank.

JRATE

Number of r a t e streams p r o p o r t i o n a l t o t h e f i r s t phase flow rate ( t h e s e are f l u o r i n a t o r s d e s c r i b e d by

a p e r c e n t removal mechanism).

Many of t h e s e are used as limits f o r implied do-loops f o r i n p u t d e s c r i b e d below.

REGION (N)

, VOLX (N) , VOLY (N) , X L I B (N) , NV (N) , NSTR(N) , I P (N) , NC (N) ,

REGA(N) , REGB(N)

, EIN(N) , N = l ,

NREG

FORMAT (A8, 2X, 3E10.0, 1 2 , 13, 1 2 , 23, A8, 2X, A8, E12.0) Each of t h e s e c a r d s d e s c r i b e s a r e g i o n .

Three are NREG c a r d s .

Explanation of v a r i a b l e s : REGION

N a m e of r e g i o n , 8 c h a r a c t e r s .

VOLX

Volume of t h e f i r s t phase, cc.

VOLY

Volume of t h e second phase, cc.

XLIB

Parameter f o r e q u i l i b r i u m ( e . g . , temperature).

lithium distribution,

Number of column a p p l i c a b l e i n t a b l e

of v a l e n c e s NV.LT.0 i m p l i e s a c o r r e c t i o n i s t o be made t o XLIB. NSTR

Number i n d i c a t i n g t h e type of e q u i l i b r i u m .

C o n t r o l s p r i n t o u t on t h e b a s i s of b i n a r y r e p r e s e n t a t i o n .

IP=O P r i n t i n g i n c l u d e s b o t h phases. IP=1 F i r s t phase i n f o r m a t i o n s t o r e d i n l e f t h a l f of l i n e . IP=2

Second phase i n f o r m a t i o n s t o r e d i n l e f t h a l f

of l i n e . IP=3 F i r s t phase i n f o r m a t i o n s t o r e d i n r i g h t h a l f of l i n e . IP=4

Second phase i n f o r m a t i o n s t o r e d i n r i g h t h a l f of l i n e .

P r i n t o u t of a l i n e o c c u r s when a r e g i o n has IP=O o r when two s u c c e s s i v e r e g i o n s have IPSO.

One of t h e s e should have a v a l u e of IP=1 o r 2 , and

t h e o t h e r should have IP=3 o r 4.

51 NC

This v a r i a b l e h a s t h r e e hexadecimal d i g i t s . f i r s t d i g i t h a s a v a l u e from 0 t o 3 .

The

Its binary

d i g i t s i n d i c a t e t h e phases whose molar volumes m u s t be i t e r a t i v e l y r e c a l c u l a t e d .

Its v a l u e s are:

0-00

N e i t h e r molar volume i s t o b e r e c a l c u l a t e d .

1-01

Second phase molar volume c a l c u l a t i o n s only.

2-10

F i r s t phase molar volume c a l c u l a t i o n s only.

3-11

Both phases r e q u i r e molar volumes c a l c u l a t i o n .

The n e x t two hexadecimal d i g i t s are used t o i d e n t i f y t h e f i r s t and second p h a s e s , r e s p e c t i v e l y .

Even when

molar volume c a l c u l a t i o n s are n o t made, t h e s e can be used f o r a s s i g n i n g t h e assumed molar volumes. REGA

N a m e of f i r s t phase t o b e used i n o u t p u t , 8 c h a r a c t e r s .

REGB

N a m e o f second phase t o b e used i n o u t p u t , 8 c h a r a c t e r s .

EIN

The number of e q u i v a l e n t s p e r c u b i c c e n t i m e t e r of t h e

materials considered assumed i n t h e second phase.

E I N is n e g a t i v e , the number of e q u i v a l e n t s p e r c u b i c c e n t i m e t e r e n t e r i n g i s used. F.

RINTO(I),

INPUT(1) , COMP(1)

, ICP(I),

I=l, NINP

FORMAT (A8, 2X, 110, E12.0, 13) Each c a r d d e s c r i b e s an i n p u t of one n u c l i d e t o a r e g i o n .

Number

of c a r d s i s NINP. Explanation of v a r i a b l e s : UNTO

N a m e of r e g i o n f e d , 8 c h a r a c t e r s .

INPUT

Numeric name (6-digit

cow

Feed rate of INPUT t o RINTO, m o l e s / s e c .

i d e n t i f i c a t i o n ) of t h e n u c l i d e .

ICP.GT.0 i d e n t i f i e s streams i n c l u d e d i n c a l c u l a t i o n

ICP

of second phase i n l e t e q u i v a l e n t d e n s i t y . G.

NSET

FORMAT (1615)

(only one v a r i a b l e r e a d ) .

NSET i s t h e number of c a r d s of t y p e H i s NSET.GT.0. H.

RDEF(1) , INDEF(1) , DCOMP(1) , I=1, NSET FORMAT ( A 8 , 2X, 110, E12.0) These c a r d s l i s t t h e p l a c e s where c e r t a i n c o n c e n t r a t i o n s are defined.

They might be bismuth i n a bismuth supply t a n k o r Q0.5

L i - B i s o l u t i o n i n a supply t a n k o f t h a t m a t e r i a l .

RDEF

Region name, 8 c h a r a c t e r s .

INDEF

Numerical name of n u c l i d e .

DCOMP

The c o n c e n t r a t i o n i n moles/cc of n u c l i d e INDEF i n r e g i o n RDEF.

RXFROM(J), RXTO(J), XRATE(J), J=1, N I N X FORMAT ( A 8 , 2X, A 8 , E12.0) RXFROM

Region name, 8 c h a r a c t e r s .

RXTO

Region name, 8 c h a r a c t e r s .

XRATE

Flow r a t e of material of t h e f i r s t phase, c c / s e c , from r e g i o n RXFROM t o r e g i o n RXTO.

RXFROM(J), RYTO(J), YRATE(J), J=1, N I N Y FORMAT ( A 8 , 2X, A 8 , E12.0) V a r i a b l e d e f i n i t i o n s are analogous t o v a r i a b l e s r e a d as type I ,

except t h a t flows are second-phase flow rates.

The c a r d s of t y p e s F , H ,

I , and J , and some of t h e c a r d s t h a t f o l l o w r e q u i r e t h e i d e n t i f i c a t i o n of r e g i o n s by name.

These are t h e r e g i o n s named by c a r d s of t y p e E.

The names are compared f o r e x a c t matches ( s p a c e s c o u n t ) .

When a name

f o r a stream d e s t i n a t i o n ( t y p e I , and J) i s n o t i n t h e l i s t of r e g i o n names, the name i s compared w i t h "DISCARD" ( l e f t j u s t i f i e d ) .

If t h i s

comparison i n d i c a t e s a match, t h e stream i s assumed t o be d i s c a r d e d . I f t h e name does n o t match, i t i s assumed t o b e d i s c a r d e d , b u t a message t o t h i s e f f e c t is printed.

Note t h a t t h e comparison w i t h t h i s key word

i s made o n l y when no s u c c e s s f u l comparison i s made t o l i s t e d r e g i o n names. Thus, t h e key word can be a l e g i t i m a t e r e g i o n i f t h e u s e r so d e s i r e s . Cards of type K, L, and M are r e a d only i f WASTE # 0. K.

RWASTE(1W) , I W = l , WASTE FORMAT (10A8) RWASTE

Names of d e s t i n a t i o n of streams t o b e s e n t t o ORIGEN.

FWASTE (IW) , I W = l ,

WASTE

FORMAT (10F8.0) WASTE M.

M u l t i p l y i n g f a c t o r t o b e used f o r these streams.

WASTE (IW), I W = l , NWASTE FORMAT (1018) KWASTE

Used by OUT0 t o make a d i s t i n c t i o n between elements i n t h e s e streams.

DET

FORMAT (20A4) The v a l u e r e a d i s n o t used. i n t h e i n p u t stream. 0.

Read only i f I 1 . G T . O

XI0

(800 v a l u e s )

FORMAT

(20A4)

This simply a l l o w s a comment c a r d

XI0 i s t h e l i s t o f c o n c e n t r a t i o n s punched from p r e v i o u s programs. The format a l l o w s a v e r y compact r e p r e s e n t a t i o n of s i n g l e prec i s i o n numbers.

One must e n s u r e t h a t t h e f i r s t number on t h e

card does n o t i d e n t i f y t h e card as an end-of-file

o r end-of-

i n f o mat i o n i n d i c a t i o n .

N e x t is read ( i f I1.GT.O): DXIN

(800 v a l u e s )

FORMAT

(20A4)

DXIN may be removal e f f i c i e n c i e s o r molar flow r a t e s ; t h e i r

v a l u e s are examined for i n d i c a t i o n s of which one t h e y r e p r e s e n t , T h i s i s n o t a fool-proof

and t h e o t h e r i s then c a l c u l a t e d . method of i d e n t i f i c a t i o n , however. I f 18.GT.0,

t h e program now r e a d s a d e s c r i p t i o n of t h e f l o w s h e e t i n t h e

format in which i t can l a t e r be punched.

I n addition t o replacing the

values i n the previously defined variables, i t replaces the values i n s e v e r a l v a r i a b l e s determined from t h e s e .

T h i s i s done t o a l l o w t h e u s e

of t h e parameter v a l u e s a r r i v e d a t in p r e v i o u s r u n s and t h u s save recalc u l a t i o n by i t e r a t i o n s . P.

Read o n l y i f NRATE.GT.0 RXNA(1) , RXNB(1) FORMAT [ 2 ( A 8 ,

, SCFACT(1) , NPORM(I), I=1, NRATE

2 X , A 8 , E12.0, 15, 5x11

Elements are assumed t o go from t h e r e g i o n RXNA t o t h e r e g i o n

RXNB a t a r a t e e q u a l t o t h e product of t h e i r c o n c e n t r a t i o n , t h e v a l u e of SCFACT, and t h e v a l u e l i s t e d i n t h e rate t a b l e o p p o s i t e t h e element symbol i n column NFORM.

I f NFORM i s

g r e a t e r than 100, t h e t a b l e used i s NFORM-100, b u t t h e t a b l e v a l u e s are changed t o 1 e x c e p t where t h e v a l u e i s 0.0.

There are JRATE c a r d s of t h i s type. REGL, REGG, I T H , COMM FORMAT (A8, 2X, A 8 , 2X, 1 5 , 5X, 2 5 A 1 ) REGL

Name of r e g i o n a t o r i g i n of t h e stream.

REGG

N a m e of r e g i o n a t d e s t i n a t i o n of t h e stream.

ITH

Column number of rate c o n s t a n t t a b l e .

COMM

25-character comment t o appear i n o u t p u t l i s t i n g .

Streams of t h i s t y p e u s e a s c a l e f a c t o r e q u a l t o t h e flow o f

material through REGL. R,

There are KRATE c a r d s of t h i s type.

REGL, REGG, AKL, AB, A S , XG, XL, ITD, ITH, ITC 'FORMAT (A8 ,2X, A 8 , 2X, 5F10.7, 213, 12) REGL, REGG, ITH are d e f i n e d as above.

AKL

Overall l i q u i d phase m a s s t r a n s f e r c o e f f i c i e n t , cm/ s e c

. 2

Bubble area, an

S u r f a c e area, cm

Thickness of s t a g n a n t g a s through which d i f f u s i o n

occurs.

Thickness of s t a g n a n t l i q u i d through which d i f f u s i o n occurs.

ITD

Column number g i v i n g g a s phase d i f f u s i v i t i e s .

ITC

Variable controlling input.

I f ITC is not 0, the

n e x t c a r d w i l l be an e x t e n s i o n of t h i s card and

w i l l r e p l a c e t h e v a l u e of t h e comment w i t h t h e f i r s t 25 c h a r a c t e r s on t h e n e x t c a r d . T h i s type of c a r d produces t h r e e r a t e streams which r e p r e s e n t m a s s t r a n s f e r t o and from t h e g a s a t t h e bubbles and a t t h e s u r f a c e , and

the t r a n s f e r of n o n v o l a t i l e n u c l i d e s from t h e gas t o t h e l i q u i d a t t h e s u r f ace.

FMT

(100 v a l u e s , 5 c a r d s r e q u i r e d )

FORMAT

(20A4)

IWT i s i n t h e form of a format i n s t r u c t i o n and i s t h e heading

p r i n t e d a t t h e t o p o f t h e t a b l e of r a t e c o n s t a n t d a t a r e a d n e x t . T.

RDATA(I), I=1,800 FORMAT

( 8 X , 8E8.0)

RDATA

Contains t h e d a t a r e f e r r e d t o by column number by v a r i a b l e s ITH, I T D , and "FORM.

The d a t a should

b e arranged on c a r d s so t h a t c a r d s are i n o r d e r of

atomic number (100 c a r d s ) w i t h t h e columns cont a i n i n g t h e numbers d e s c r i b e d p r e v i o u s l y .

These

can be d i f f u s i v i t i e s , Henry's l a w c o n s t a n t s , PR/(l-PR)

(where PR i s p e r c e n t removal), o r any

o t h e r c o n s t a n t s which might v a r y w i t h atomic number. A f t e r t h e s e c a r d s are r e a d , i n p u t i s r e a d by s u b r o u t i n e EQKN and s u b r o u t i n e VOLUME, r e s p e c t i v e l y .

INPUT TO EQKN

EQKN r e a d s a series of card p a i r s from u n i t 50 t o a s s i g n v a l u e s t o

t h e d i s t r i b u t i o n c o e f f i c i e n t s throughout t h e p r o c e s s i n g p l a n t .

The

cards read contain: A.

LZ, NS, NT, AN, A, B, ENAME

FORMAT (13, 2 1 2 , 8X, F2.0,

lox,

E8.0,

2X, E 8 . 0 ,

3 3 X , A2)

LZ2, NS2, REF

FORMAT (13, 1 2 , 75A1) LZ = atomic number NS = number i d e n t i f y i n g t h e t y p e of e q u i l i b r i u m corresponds

t o NSTR i n t h e d e s c r i p t i o n of r e g i o n s . NT = i d e n t i f i e s t h e t y p e of e q u a t i o n involved.

End of i n p u t , r e t u r n

loglo(D)

D = A

394

log(P) = A / ( 2 7 3 . 2

Distribution coefficient

XLIB

Constant r e a d with r e g i o n d e s c r i p t i o n s

P a r t i a l pressure

= (AN) loglo

XLIB

+ XLIB) +

A+B/T (in

AN, A, B = d a t a

ENAME = e l e m e n t a l symbol name f o r o u t p u t of e q u i l i b r i u m LZ2, NS2 = n o t used

REF = 75 character r e f e r e n c e f o r d a t a i n t h e f i r s t card. Two s p e c i a l f l a g s are recognized. 102, t h e v a l u e of NT i s assumed t o b e 2.

I f t h e element atomic number i s

In a d d i t i o n , a l l elements are

a s s i g n e d t h e same d i s t r i b u t i o n c o n s t a n t f o r t h e d i s t r i b u t i o n type NS. T h i s o v e r r i d e s p r e v i o u s i n p u t , b u t i t i s assumed t h a t e x c e p t i o n s follow. T h i s d e v i c e g r e a t l y reduces t h e amount of i n p u t .

I f t h e atomic number

LZ i s 101, no d a t a are taken from t h e c a r d s , b u t t h e v a r i a b l e REF i s assumed t o be a page heading f o r t h i s t y p e of e q u i l i b r i u m .

For p r o p e r

output t a b u l a t i o n , i t i s assumed t h a t a l l c a r d s s p e c i f y i n g a p a r t i c u l a r

type of e q u i l i b r i u m are t o g e t h e r and t h a t t h e s e are s e p a r a t e d by t i t l e changes. The program p r i n t s t h e form of t h e e q u a t i o n i n the o u t p u t t a b l e . The space allowed between c o n s t a n t s on i n p u t c a r d s may be used t o type t h e e q u a t i o n t h a t will b e used.

INPUT TO VOLUME

A l l i n p u t t o VOLUME i s r e a d from u n i t 2 and i s used t o make estimates

of molar volumes and a t a b l e of v a l e n c e s .

NTA, NTB FORMAT (3212) Each v a r i a b l e h a s 1 6 elements corresponding t o t h e v a l u e of t h e second and t h i r d hexadecimal d i g i t of NC, which corresponds t o r e g i o n s and i d e n t i f i e s t h e phases p r e s e n t .

The values

i d e n t i f y t h e column numbers i n VOLC. B.

VOLC

FORMAT (8X, 8E8.0)

E i g h t hundred v a l u e s are r e a d , corresponding t o 8 v a l u e s each

(1 c a r d ) f o r t h e elements i n i n c r e a s i n g o r d e r of atomic number. A l i s t i n g g i v e s 8 columns, which correspond t o p h a s e s , and 100

rows, which correspond t o elements.

VOLC c o n t a i n s t h e c o n t r i -

b u t i o n of t h e elements t o t h e molar volume of each of t h e phases.

VAL

FORMAT (8X, 8E8,O) VAL h a s 800 v a l u e s arranged s i m i l a r l y t o VOLC.

The v a l u e s of

VAL are v a l e n c e s f o r u s e i n c o n t a c t o r s , w i t h columns being

r e f e r r e d t o by t h e v a r i a b l e NV.

APPENDIX C:

OUTPUT

Output Produced by MATADOR and i t s S u b r o u t i n e s

Output from AMATRX:

(1) Nuclear L i b r a r y (2)

Summary of f i s s i o n y i e l d s

The f i s s i o n y i e l d s are summarized by mass c h a i n s i n two groups, and cumulative t o t a l s are given a f t e r each group f o r p a r t i c l e and mass y i e l d s as i n d i c a t e d by t h e n u c l e a r l i b r a r y . B.

Output from MATADOR on t h e f i r s t c a l l : MATADOR produces a l i s t of t h e i n p u t v a r i a b l e s .

Output from CHEMPL on t h e f i r s t c a l l : CHEMPL produces an element-by-element

t a b l e of removal times u s i n g

t h e s t a r t i n g e f f i c i e n c i e s , the removal time given by NTLME, and t h e u n i t s given by PUNIT.

The u s e r i s r e s p o n s i b l e f o r e n s u r i n g agreement of NTIME

and PUNIT w i t h t h e v a r i a b l e TIME i n u n i t s of seconds. D.

Output from RESULT produced each time RESULT i s c a l l e d :

(1) A t a b l e i s produced t h a t l i s t s t h e c o n c e n t r a t i o n f o r each n u c l i d e i n moles p e r c u b i c c e n t i m e t e r and atom f r a c t i o n , i t s c o n t r i b u t i o n t o p o i s o n i n g , i t s i n v e n t o r y i n c u r i e s , i t s cont r i b u t i o n t o t h e power d e n s i t y , t h e f r a c t i o n of that power produced as gamma h e a t , i t s chemical p r o c e s s i n g rate, and i t s mole f r a c t i o n i n t h e i n l e t stream as determined by t h e process i n g p l a n t code. (2)

T h i s t a b l e is followed by a l i s t of c a l c u l a t e d v a l u e s which i n d i c a t e r e a c t o r performance.

(3)

This i n f o r m a t i o n i s summarized f o r t h e 25 g r e a t e s t v a l u e s under most of t h e headings i n t h e f i r s t t a b l e ; a n o t h e r t a b l e i s given p r o v i d i n g t o t a l s f o r each stream.

(4)

A summary i s p r e s e n t e d t h a t compares thorium burnup rate w i t h

t h e weight of f i s s i o n p r o d u c t s and a c t i n i d e s removed.

(5)

A summary t a b l e i s given t h a t l i s t s t h e t o t a l rate of chemical

p r o c e s s i n g f o r each element.

(6)

A n o t e i s i n c l u d e d on t h e number of c a l l s t o MATADOR.

(This

i s o n l y a c c u r a t e i f KEE i s c a l l e d e v e r y time a p a s s i s made through MATADOR. ) Output from t h e P r o c e s s i n g P l a n t Program

P r i n t e d Output

The o u t p u t b e g i n s w i t h o u t p u t o b t a i n e d by the f i r s t c a l l t o MATADOR. The program t h e n p r i n t s the i n p u t v a r i a b l e s .

T a b l e s appear t h a t d e s c r i b e

a l l r e g i o n s , l i s t - f e e d streams and s p e c i f i e d c o n c e n t r a t i o n s , d e s c r i b e flowing streams i n each phase and streams d e f i n e d by r a t e c o e f f i c i e n t s , i n d i c a t e e x p r e s s i o n s f o r d i s t r i b u t i o n c o e f f i c i e n t s , and compute a d d i t i v e molar volumes and v a l e n c e s .

A number of i n t e r m e d i a t e c a l c u l a t e d r e s u l t s are p r i n t e d t o monitor t h e p r o g r e s s of t h e c a l c u l a t i o n s .

Between i t e r a t i o n s , t h e r e i s a l i s t

of t h e 50 n u c l i d e s w i t h t h e g r e a t e s t r e l a t i v e change i n c o n c e n t r a t i o n r e t u r n i n g t o t h e r e a c t o r , and t h e c o n c e n t r a t i o n s and t h e r e l a t i v e changes.

Upon convergence, t h i s l i s t i s p r i n t e d f o r a l l n u c l i d e s .

The l i t h i u m d i s t r i b u t i o n X L I B c a l c u l a t e d by VOLUME i s a l s o p r i n t e d between i t e r a t i o n s , w i t h t h e change i n e q u i v a l e n t d e n s i t y e n t e r i n g

each s t a g e f o r which t h e d i s t r i b u t i o n c o e f f i c i e n t s are r e c a l c u l a t e d . A s a means of m o n i t o r i n g t h e p r o g r e s s of c a l c u l a t i o n s , t h e t i m e i n

hundredths of a second i s p r i n t e d a t v a r i o u s p o i n t s i n the c a l c u l a t i o n . When t h e t i m e l i m i t o r convergence c r i t e r i o n i s m e t , a n o t h e r c a l l

i s made t o RESULT t o o b t a i n o u t p u t summarizing the r e a c t o r c a l c u l a t i o n s . A p a r t i a l l i s t i n g of t h e f l o w s h e e t d e s c r i p t i o n i s made which r e f l e c t s t h e new flow r a t e s used.

A t a b l e , whose heading g i v e s t h e h a l f - l i f e

and removal t i m e of t h e n u c l i d e , i s i n c l u d e d f o r each n u c l i d e i n t h e library.

The t a b l e l i s t s t h e c o n c e n t r a t i o n (moles/cc)

, the

inventory

( i n moles and i n c u r i e s ) , and t h e t o t a l flow r a t e ( i n moles/day) of t h e n u c l i d e i n each phase of each r e g i o n in t h e p r o c e s s i n g p l a n t .

The t a b l e s

are s h o r t e n e d by t h e combining of one-phase r e g i o n s as i n d i c a t e d by t h e input variable, IP.

Each of t h e s e t a b l e s i s followed by a l i s t of a l l

d i s c a r d rates i n moles p e r day, and a l i s t of flow rates i n moles p e r day i n a l l streams which do n o t r e p r e s e n t t h e t o t a l f l o w of one phase out of a region. by t h e i r names.

I n a l l of t h e s e , t h e r e g i o n s and phases are i d e n t i f i e d When two r e g i o n s each have one phase t o b e l i s t e d on

t h e same l i n e , as s p e c i f i e d by I P , t h e r e g i o n name of the f i r s t of t h e two r e g i o n s in t h e i n p u t i s used t o a p p l y t o both.

This output i s repeated

i n a summary t a b l e f o r each element i n which t h e t o t a l s are given f o r t h e v a l u e s in t h e p r e v i o u s t a b l e s .

These t a b l e s are followed by a t a b l e g i v i n g

t h e t o t a l s f o r a l l materials. T h i s series i s followed by a series of t a b l e s which g i v e heat generat i o n rates i n each phase of each r e g i o n .

For each t a b l e , the 50 n u c l i d e s

w i t h t h e h i g h e s t h e a t g e n e r a t i o n rate a t t h a t p o i n t in t h e f l o w s h e e t are l i s t e d along w i t h t h e i r c o n t r i b u t i o n t o t o t a l heat g e n e r a t i o n r a t e , gamma

63 h e a t g e n e r a t i o n rate, and b e t a h e a t g e n e r a t i o n rate.

Each of t h e s e is

g i v e n as t o t a l power i n megawatts, and as power d e n s i t y of k i l o w a t t s p e r

liter.

These are t o t a l e d f o r a l l n u c l i d e s , and an a d i a b a t i c temperature

rise i n 'C p e r minute is p r i n t e d . I n a d d i t i o n t o p r i n t e d o u t p u t , the program p r e p a r e s punched o u t p u t

which i n c l u d e s r e a c t o r c o n c e n t r a t i o n s and p r o c e s s i n g p l a n t removal t i m e s f o r a l l n u c l i d e s , and a d e s c r i p t i o n of the flowsheet.

T h i s output, i f

r e q u e s t e d by p o s i t i v e v a l u e s f o r t h e i n p u t v a r i a b l e s I 2 and 1 6 , can be used l a t e r t o e s s e n t i a l l y c o n t i n u e t h e c a l c u l a t i o n s from t h e p o i n t a t which o u t p u t was o b t a i n e d .

The r e a c t o r c o n c e n t r a t i o n s and p r o c e s s i n g

p l a n t removal t i m e s can a l s o b e used t o e l i m i n a t e many of t h e i t e r a t i o n s r e q u i r e d when a flowsheet with similar performance i s used.

Output t o b e Used by ORIGEN

A copy of ORIGEN

7 w a s o b t a i n e d , and m o d i f i c a t i o n s w e r e made t o allow

t h e p r i n t i n g of only t h o s e t a b l e s s p e c i f i e d by i n p u t v a r i a b l e s , t o a l l o w input formats to be used which r e q u i r e flow rates i n a form convenient

f o r o u t p u t by t h e p r o c e s s i n g p l a n t code, and t o a l l o w i n p u t t o b e r e a d

from a s o u r c e o t h e r t h a n the c a r d r e a d e r ,

Output i n t h i s form d e s c r i b i n g

a series of streams i s produced on u n i t 28 f o r l a t e r i n p u t t o ORIGEN.

I n a l l programs used t o d a t e , t h i s o u t p u t w a s w r i t t e n on a d i s c f i l e r e a d by ORIGEN i n a second j o b s t e p . The first streams i n c l u d e d are s p e c i f i e d by the i n p u t v a r i a b l e s WASTE, RWASTE, FWASTE, and KWASTE.

F o r o u t p u t stream I W ENWASTE), t h e

v a r i a b l e RWASTE(1W) g i v e s t h e name of t h e d e s t i n a t i o n of all streams t h a t

are i n c l u d e d .

Streams t h a t are d i s c a r d e d may b e s e n t t o a n o n e x i s t e n t

64 r e g i o n name i n t h e l i s t of waste r e g i o n s .

The i n c l u d e d streams are

f u r t h e r decreased by t h e use of KWASTE(1W) t o s p e c i f y t h e phase as f o l l o w s : MJASTE'LT'O

o n l y f i r s t - p h a s e streams are c o n s i d e r e d ,

KWASTE*EQ*O streams from e i t h e r phase are c o n s i d e r e d ,

KWASTE'GT'O

o n l y second-phase streams are considered.

The molar flows of streams meeting t h e s e requirements are added and m u l t i p l i e d by ABS[FWASTE(IW)] b e f o r e being sent t o ORIGEN and i n c l u d e d i n the t o t a l ,

F o r t h e s p e c i a l case of KWASTE(IW)*NE*O,and FWASTE(1W)

between -0.001 and 0.0, t h e v a l u e of FWASTE(1W) i s 0.001 when c o n s i d e r i n g i s o t o p e s of neptunium.

Streams are then o u t p u t which r e p r e s e n t 5 l i t e r s

of s a l t s t i c k i n g t o t h e g r a p h i t e d i v i d e d by t h e number of days i n 4 years, t h e s e r e p r e s e n t d a i l y d i s c a r d rates of n o b l e metals from t h e r e a c t o r c o r e , n o b l e g a s e s from t h e s a l t d r a i n t a n k , and n o b l e m e t a l s from o u t s i d e t h e r e a c t o r core.

All of t h e s e , e x c e p t t h e s a l t s t i c k i n g t o t h e g r a p h i t e ,

are added t o t h e flow o u t p u t streams w i t h FWASTE(IW)*GT'O; t h e t o t a l i s o u t p u t t o r e p r e s e n t t o t a l d a i l y waste o t h e r t h a n g r a p h i t e removal. F i n a l l y , t h e d a i l y rate of d e p o s i t i o n of materials on the g r a p h i t e i s o u t p u t as a stream t h a t ORIGEN will assume i s i r r a d i a t e d f o r 4 years,

ORNL/TM-4210 D i s t . Category UC-76

INTERNAL DISTRIBUTION

MSRP D i r e c t o r ' s O f f i c e C. E. Bamberger 4. M. Bender 5. R. E. Brooksbank 6. C. H. Brown, Jr. 7. W. D. Burch 8. W. L. Carter 9. H. D. Cochran, Jr. 10. R. M. Counce 11. F. L. C u l l e r 1 2 . J. M. Dale 13. F. L. Daley 14. J. R. DiStefano 15. R. L. E g l i , ERDA-OR0 16. J. R. Engel 17. G. G. Fee 18. D. E. Ferguson 1 9 . L. M. F e r r i s 20. A. T. Gresky 21. W. R. G r i m e s 22. W. S. Groenier 23. R. H. Guymon 24. B. A. Hannaford 25. R. F. Hibbs J . R. Hightower, Jr. 26-27. 28. V . A. Jacobs C. W. Kee 29-43. 44. 0. L. Keller A. D. Kelmers 45 46. H. T. Kerr 47. J . A. Lenhard, ERDA-OR0 1-2.

48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76-77. 78. 79-81. 82.

H. G. MacPherson, UT R. E. MacPherson A. P. Malinauskas C. L. Matthews, ERDA-OR0 G. T. Mays H. E. McCoy T. W. P i c k e l H. Postma M. W. Rosenthal H. C. Savage C. D. S c o t t J. T. Shannon M. J. Skinner F. J. Smith J . W. S n i d e r I. Spiewak M. G. S t e w a r t D. B. Trauger D. Y. V a l e n t i n e J. W. Wachter J . S. Watson A. M. Weinberg, ORAU J. R. Weir M. E. Whatley J. C. White M. K. Wilkinson R. G. Wymer E. L. Youngblood C e n t r a l Research L i b r a r y ( 2 ) Document Reference S e c t i o n Laboratory Records (3) Laboratory Records (LRD-RC)

' I

CONSULTANTS AND SUBCONTRACTORS

83.

84. 85. 86. 87.

J. C. E. W. R.

C. Frye

H. A. K. B.

Ice Mason Davis Richards

EXTERNAL DISTRIBUTION

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Research and T e c h n i c a l Support D i v i s i o n , ERDA, Oak Ridge Operations O f f i c e , P. 0. Box E , Oak Ridge, Tenn. 37830 D i r e c t o r , Reactor D i v i s i o n , ERDA, Oak Ridge O p e r a t i o n s O f f i c e , P. 0. Box E , Oak Ridge, Tenn. 37830 D i r e c t o r , ERDA D i v i s i o n of Reactor Research and Development, Washington, D.C. 20545 For d i s t r i b u t i o n as shown i n TID-4500 under UC-76, Molten S a l t Reactor Technology