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This repQii was piep2:ed as a; account of w x k sponsors2 hy an agency of the Unitcd States Government Neii l iei the !J nite ihereQf, nor m y of thc:: emp!3yes, ii-,akes assumes any lepr?! liability or respoiisiijility vsefulness of any information, apparatus. reprssznts that i ts usr.?-~?uld nui i~if<,ngz private!:. cwxc! rights. Ec f~rcncc herein to any specific Comrribiiial paduc t . process nr scfwce by trade name, tra& manufn-iurec. or other doss not necessarily constltutc or imply its eidorse;nen!. recoImix;ldation, or favoring by the Llfiitk>d States Gnvcrnii-te!.r; or any egency thernc!!. The v ~ ~ i i ' s and opil-,ions of authui-s axpressed heieln do not necessarily siatn 0: reflect ihoso c! t i le Cnited States Gweii i i i len? or any cgzncy thered.
ORNL/TM-9694 D is t . Category: UC-70 (Waste)
Engi n e e r i ng Physics and Mathematics D i v i s i s n
GRESS TRANSLATION OF THE ORIGENZ CODE
Franco is G. Pin
and
Q. Q. Wright*
*Cornput i ng and T e l ecomrniiunicat i ons D i v i s i o n
Date Pub l ished : May 1986
?repared f o r t he O f f i c e o f Nuc lear Waste I s o l a t i o n
Battel le Mernori a1 I n s t i t u t e 505 King Avenue
Columbus, OH 43201-2693
by t h e OAK R I D G E VATIdNAL LABORATORY
ilak f i idye, Tennessee 37831 $3 p e r a t ed by
M a r t i n M a r i e t t a Energy Sys tem, Inc. f o r t h e
U.S. DEPARTMENT OF ENERGY under c o n t r a c t No. DE- ACO5-84UK21400
3 4 4 5 6 0138995 7
TABLE OF CONTENTS
L I S T OF EXHI13ITS .................................................... V
ABSTRACT ............................................................ v i i
I . INTQODUCTION .................................................. 1
11. CODE PREPARATION .............................................. 3
111. AUTOMATED S E N S I T I V I T Y CALCULATIONS ............................ 7
I V . S E N S I T I V I T Y VERIFICATION STUDY ................................ 1 5
V . CONCLUSIONS 29
REFERENCES .......................................................... 31
APPENDIX ............................................................ 33
...................................................
iii
L I S T OF EXHIBITS
E x h i b i t 1. Command and m a t e r i a l composi t ion i n p u t f i l e for
E x h i b i t 2. ORIGEN2 o u t p u t and s e n s i t i v i t i e s t o parameters 1, 2, 3
sample problem .......................................... f o r sample problem ......................................
Exhl ’b i t 3. OKIGEN2 o u t p u t and s e n s i t i v i t i e s t o parameters 4, 5, 6 f o r sample problem . . . . . . .O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E x h i b i t 4. S e n s i t i v i t i e s t o parameter 1 approximated from forward p e r t u r b a t i o n a n a l y s i s .................................
E x h i b i t 5. S e n s i t i v i t i e s t o parameter 2 approximated from forward p e r t u r b a t i o n a n a l y s i s ...................................
E x h i b i t 6. S e n s i t i v i t i e s t o parameter 3 approximated from fo rward p e r t u r b a t i o n a n a l y s i s ........*........................
E x h j b i t 7. S e n s i t i v i t i e s t o parameter 4 approximated from fo rward p e r t u r b a t i o n a n a l y s i s .................................
E x h i b i t 8. S e n s i t i v i t i e s t o parameter 5 approximated f r o m forward p e r t u r b a t i o n a n a l y s i s ....................................
E x h i b i t 9. S e n s i t i v i t i e s t o parameter 6 approximated from forward p e r t u r b a t i o n a n a l y s i s
8
10
12
16
18
20
22
24
26
V
ABSTRACT
ORIGEW2 i s a w i d e l y used p o i n t - d e p l e t i o n and r a d i o a c t i v e - decay comput.er code f o r use i n s i m u l a t i n g nuc lea r fue l cyc les and/or spent f u e l c h a r a c t e r i s t i c s . I n t y p i c a l a p p l i c a t i o n s the code c a l c u l a t e s cha in b u i l d u p and decay o f more than 1600 r a d i o - n u c l i d e s and elements. Th is r e p o r t descr ibes t h e a d d i t i o n t o t h e OKIGENZ code of an automated s e n s i t i v i t y c a l c u l a t i o n capa- b i l i t y by means of the GRESS p recompi le r . The GRESS p recomp i le r uses computer c a l c u l u s t o au tomat ica l l y enhance FORTRAN computer codes w i t h d e r i v a t i v e - t a k i n g capabi 1 i t i e s . From these d e r i v a t i v e s generated c o n c u r r e n t l y w i t h t h e normal r e s u l t s , s e n s i t i v i t i e s o f any v a r i a b l e used i n t h e code w i t h respec t t o any o t h e r v a r i a b l e o r i n p u t parameter can r e a d i l y be obta ined. The added s e n s i t i v i t y c a l c u l a t i o n c a p a b i l i t y i s v e r i f i e d on a sample problem i n v o l v i n g f u e l burnup under s p e c i f i e d power, r a d i o a c t i v e decay, and m a t e r i a l i r r a d i a t i o n under s p e c i f i e d f l u x . The accuracy o f t h e GRESS r e - s u l t s i s demonstrated us ing comparisons w i t h t h e r e s u l t s o f per - t u r b a t i o n analyses.
v i i
I. INTRODUCTION
I
ORIGEN2l i s a p o i n t - d e p l e t i o n and rad ioac t i ve -decay computer code
f o r use i n s i m u l a t i n g n u c l e a r f u e l c y c l e s and c a l c u l a t i n g t h e n u c l i d e
compos i t ions and c h a r a c t e r i s t i c s o f m a t e r i a l s conta ined t h e r e n. It i s a
r e v i s e d ve rs ion o f t h e o r i g i n a l ORIGEN computer codeza5 which was deve l -
oped a t t h e Oak Ridge Na t iona l Labora tory i n t h e e a r l y 1970 's The r e -
v i s i o n s i n c l u d e updates of t h e r e a c t o r models, c ross sec t i ons , f i s s i o n
p roduc t y i e l d s , decay data, and decay photon data. The l i s t o f r e a c t o r s
t h a t can be s imu la ted i n c l u d e s p r e s s u r i z e d water reac to rs , b o i l i n g water
r e a c t o r s , l i q u i d - m e t a l f a s t breeder r e a c t o r s , and Canada deuter ium uran-
i um reac to rs .
The code uses a m a t r i x exponen t ia l i w t h o d to so lve a l a r g e system of
coupled, l i n e a r , f i r s t o r d e r o r d i n a r y d i f f e r e n t i a l equat ions w i t h con-
s t a n t c o e f f i c i e n t s . It has been v a r i a b l y dimensioned t o a l l o w t h e user
t o t a i l o r t h e s i z e of t he executab le module t o the problem s i z e and/or
t h e a v a i l a b l e computer space. The da ta used by t h e code i s o f two types,
g e n e r i c da ta which i s p a r t o f t h e code package and i s read f rom a s e r i e s
o f l i b r a r y f i l e s d e s c r i b i n g t h e n u c l i d e cha in c h a r a c t e r i s t i c s , c ross
sec t i ons , f i s s i o n produc t y i e l d s , decay da ta and decay photon data; and
problem s p e c i f i c da ta i n c l u d i n g t h e compos i t ion o f the m a t e r i a l s i n t h e
r e a c t o r and a s e r i e s of commands d e s c r i b i n g , s tep by s tep, t h e nuc lea r
fuel c y c l e scenar ios cons idered i n t h e problem. The ou tpu t o f t h e code
c o n s i s t s o f vec tors t h a t c o n t a i n t h e amount o f each rad ionuc? i d e be ing
cons idered i n t h e problem. A v e c t o r i n ORIGENZ i s a one-dimensional a r -
r a y which i s p r i n t e d as a s i n g l e column o f numbers i n t h e ou tpu t . W i t h i n
t h e vec tors , t h e n u c l i d e s are grouped i n t o t h r e e segments as f o l l o w s :
1
2
1. A c t i v a t i o n products , which c o n s i s t o f n e a r l y a l l n a t u r a l l y o c c u r i n g nuc l i des , t h e i r neut ron abso rp t i on products , and t h e decay daughters o f these products . Th is segment i s p r i n c i p a l l y used t o handle s t r u c t u r a l m a t e r i a l s (e.g. l i r c a l o y ) and f u e l i m p u r i t i e s .
2. Ac t i n ides , which c o n t a i n t h e i so topes o f t h e elements tho r ium (a tomic number 90) th rough e i n s t e i n i u m (a tomic number 99) t h a t appear i n s i g n i f i c a n t amoiints i n d ischarged r e a c t o r f u e l s p l u s t h e i r decay daughters.
3. F i s s i o n products , which c o r l s i s t of nuc l i des produced by ac t in ides f i s s i o n p l u s t h e i r decay and capture products .
Fo r t h e casss considered here, each vec to r conta ined c o n c e n t r a t i o n values
f a r 688 a c t i v a t i o n products , 129 a c t i n i d e s and daughters, and 879 f i s s i o n
products .
3
11. CODE PREPARATION
The GRESS p recomp i le r and i t s c a p a b i l i t i e s have been descr ibed i n
I n essence, GKESS reads and d e t a i l s i n severa l o t h e r pub l i ca t i ons .6 -8
analyzes every statement i n t h e FORrRAN source code t o be t r a n s l a t e d and
a u t o m a t i c a l l y adds t h e l i n e s o f cod ing t h a t are necessary t o c a l c u l a t e
t h e d e r i v a t i v e s o f t h e s t o r e d q u a n t i t y w i t h respec t t o the v a r i a b l e s used
i n i t s computation. It i s , t h e r e f o r e , e s s e n t i a l t h a t t h e source code be
w r i t t e n u s i n g a forniat compat ib le w i t h t h a t recogn izab le by GRESS. Th is
i s t h e case, i n genera l , i f t h e code has been w r i t t e n u s i n g r e g u l a r
FORTRAN syntax. I n t h e case o f ORIGEN2, on ly minor changes were r e q u i r e d
t o make t h e code compat ib le w i t h t h e GRESS precompi ler .6
These changes a re descr ibed be l ow:
1. I n i t s p resent form, t h e GRESS preco i i ip i le r does no t recogn ize sub- s c r i p t s t h a t are indexed v a r i a b l e s o r express ions. Th is was e a s i l y remedied by r e p l a c i n g s tatements o f t h e form:
A = 8 ( C ( U ) ) by INDEX = C(9) A = B (INDEX)
and rep1 a c i ny s tatements o f the form:
A = B (C+D) bY INDEX = C+D A = B (INDEX)
2. A l l DOUBLE P R E C I S I O N d e f i n i t i o n s tatements were rep laced by REAL "8 d e f i n i t i o n statements.
3 . A l l INTEGER *2 d e f i n i t i o n s tatements were rep?aced by INTEGER d e f i n i t i o n statements.
4. Colons and semicolons were rep laced by blank charac ters .
4
5. Arrays w i t h 3 ( o r more) s u b s c r i p t s were rep laced by a r rays w i t h 1 s u b s c r i p t coupled w i t h a statement t o compute t h e index. In ORIGEN2 o n l y one such a r r a y was encountered (XCUM i n t h e sub rou t ine OUTPUT).
6. Statements u s i n g an express ion i n t h e argument l i s t o f a c a l l t o a s u b r o u t i n e were m o d i f i e d by c a l c u l a t i n g and s t o r i n g t h e express ion i n a v a r i a b l e , then us ing t h e v a r i a b l e i n t h e argument l i s t . An example o f t h i s m o d i f i c a t i o n occurs a t card #3437 i n ORIGEN2 where JTYP +2 was used as an argument. The statement JTYP2 = JTYPc2 was i n s e r t e d b e f o r e t h e c a l l t o t h e sub rou t ine and JTYP2 was used i n t h e argument l i s t .
4 . A r i t h m e t i c statement f u n c t i o n were rep laced by a c a l l t o a f u n c t i o n an i n s e r t o f t h e f u n c t i o n subprogram. subprogram and
These changes i n v o
e f f e c t on t h e resu
t h e r e s u l t s o f t h e
were i d e n t i c a l .
ved FORTRAN language o p t i m i z a t i o n o n l y and had no
t s o f t h e code. This was v e r i f i e d by check ing t h a t
code be fo re and a f t e r t h e m o d i f i c a t i o n s were made
In a d d i t i o n t o the m o d i f i c a t i o n s desc r ibed above, minor m o d i f i c a t i o n s
were made i n t h e code ou tpu t r o u t i n e s t o f a c i l i t a t e t h e s e n s i t i v i t y c a l -
c u l a t i o n v e r i f i c a t i o n s tud ies . The ou tpu t formats were changed t o
i n c l u d e 6 s i g n i f i c a n t d i g i t s and a l low p r i n t i n g o f normal ized s e n s i t i v i t y
c o e f f i c i e n t s c o n c u r r e n t l y w i t h t h e p r i n t i n g o f r e g u l a r output . Software
was a l s o developed t o a u t o m a t i c a l l y c a l c u l a t e , s to re , and p r i n t s e n s i t i v -
i t i e s d e r i v e d from p e r t u r b a t i o n runs.
A more s e r i o u s problem n e c e s s i t a t i n g code m o d i f i c a t i o n was encountered
w i t h t h e ORIGENT code d u r i n g t h e v e r i f i c a t i o n phase. This problem does
n o t r e l a t e t o GRESS c o i n p a t i b i l i t y and deals w i t h a l o s s o f p r e c i s i o n
caused by t r u n c a t i o n e r r o r s i n t h e c a l c u l a t i o n o f t h e c o n c e n t r a t i o n o f
c e r t a i n nuc l i des . The l o s s of p r e c i s i o n was found t o occur i n a nested
s e r i e s of DO loops i n t h e sub rou t ine MATREX. 'To remedy t h e problem, t h e
5
v a r i a b l e s CIMO, CIMB, C I M N I , TON, AP and T were changed l o c a l l y t o REAL
"8 va r iab les . Much b e t t e r r e s u l t s were ob ta ined w i t h t h i s c o n f i g u r a t i o n
and i t i s suggested t h a t t h i s m o d i f i c a t i o n be proposed t o t h e ORIGENZ
code authors.
7
111, AUTOMATED SENSITIVITY CALCULATIONS
With t h e m o d i f i c a t i o n s desc r ibed p r e v i o u s l y , t h e ORIGENZ was suc-
c e s s f u l l y t r a n s l a t e d th rough t h e GRESS precornpi l e r .
c i s i o n GRESS l i b r a r y was used f o r t h i s t r a n s l a t i o n a l l o w i n g p ropaga t ion
o f d e r i v a t i v e s th rough mixed s i n g l e and double p r e c i s i o n va r iab les . A
sample problem i n v o l v i n g burnup of one m e t r i c t o n o f f u e l under s p e c i f i e d
power, r a d i o a c t i v e decay, and i r r a d i a t i o n o f Z i r c a l o y under s p e c i f i e d
f l u x was used f o r t h e s e n s i t i v i t y c a l c u l a t i o n and v e r i f i c a t i o n study. A
l i s t i n g o f t h e command i n p u t f i l e i n c l u d i i g f u e l and Z i r c a l o y compos i t ion
i s g iven i n E x h i b i t 1. S i x parameters, r e p r e s e n t a t i v e o f t h e va r ious
da ta types used by O R I G E N 2 were s e l e c t e d f o r c a l c u l a t i o n o f s e n s i t i v i -
t i e s . Three parameters, t h e c ross -sec t i ons f o r 235U f i s s i o n ( P l ) , 2 3 8 U
c a p t u r e (P2), and 23gPu (P3) f i s s i o n , are i n p u t f ro in c r o s s - s e c t i o n
l i b r a r i e s t h a t a re p a r t o f t h e ORIGENZ code package, and t h r e e parameters,
t h e Z i r c a l o y i r r a d i a t i o n f l u x ( P 4 ) , t he fue l burnup power ( P t i ) , and t h e
235U assay (P6) a re i n p u t froin t h e command and m a t e r i a l compos i t ion i n p u t
f i l e shown i n E x h i S i t 1. Normalized s e n s i t i v i t y c o e f f i c i e n t s o f a l l
r a d i o n u c l i d e concen t ra t i ons r e p r e s e n t i n g d ischarge c h a r a c t e r i s t i c s a f t e r
i r r a d i a t i o n o f Z i r c a l o y (Vl) and fue l burnup (V2) t o the 6 parameters
mentioned above were c a l c u l a t e d u s i n g t h e GRESS procedure- Examples o f
p r i n t o u t o f these s e n s i t i v i t i e s fo r t he f i r s t 104 a c t i v a t i o n produc ts
( a t o t a l o f about 20352 s e n s i t i v i t i e s were c a l c u l a t e d ) a re shown i n
E x h i b i t s 2 and 3. The f i r s t two columns g i v e t h e r e s g l t s o f t h e ORIGEN2
code f o r t h e performance ineasures V 1 and V2. The nex t s i x columns w i t h
headi ngs of t h e type V i Pj g i ve t h e normal i zed scns i t i v i t y coef f i c i e n t s
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pj a V i I__I_____ o f t h e performance measure V i w i t h respec t t o t h e parameter P j . V i a P j S e n s i t i v i t y c o e f f i c i e n t s were found e i t h e r i d e n t i c a l l y zero, i n d i c a t i n g
no i n f l u e n c e o f t he parameter on t h e n u c l i d e concen t ra t i on , o r w i t h mag-
n i t u d e rang ing froiii loe2 t o 2.0 x 10’.
f i c i e n t s t a t h e s p e c i f i e d power and t h e s p e c i f i e d f l u x were found t o be
t h e l a r g e s t , i n d i c a t i n g t h a t these parameters should be c a r e f u l l y se lec ted
f o r a s i m u l a t i o n study s ince they are t h e most l i k e l y t o propagate l a r g e
u n c e r t a i n t i e s t o t h e model r e s u l t s .
In general, s e n s i t i v i t y coe f -
15
IV. SENSITIVITY VERIFICATION STUDY
Since a n a l y t i c a l s o l u t i o n s are no t f e a s i b l e o r p r a c t i c a l f o r
problems such as those t r e a t e d by t h e ORIGENZ code, t h e v e r i f i c a t i o n of
t h e GRESS s e n s i t i v i t y c a l c u l a t i o n s was performed u s i n g p e r t u r b a t i o n
a n a l y s i s methods. I t should be noted, however, t h a t for codes i n v o l v i n g
decay and b u i l d u p o f l a r g e chains o f rad ionuc? ides , p e r t u r b a t i o n a n a l y s i s
u s i n g fo rward ( p o s i t i v e ) parameter p e r t u r b a t i o n s o r l a r g e parameter per -
t u r b a t i o n va lues p r o v i d e o n l y a poor approx imat ion o f t h e g r a d i e n t s a t
t h e s o l u t i o n p o i n t . Th is problem was overcome here by us ing smal l param-
e t e r p e r t u r b a t i n n val ues (-1% t o 1%) and, when necessary, approx imat ing
t h e g rad ien ts a t t h e s o l u t i o n p o i n t by u s i n g fo rward ( p o s i t i v e ) and back-
ward ( n e g a t i v e ) parameter p e r t u r b a t i o n values. Sof tware was designed t o
automate t h e c a l c u l a t i o n s of t h e approximate s e n s i t i v i t y c o e f f i c i e n t s
f rom forward p e r t u r b a t i o n r e s u l t s . Examples o f t h e r e s u l t s p r i n t o u t f o r
t h e f i r s t 104 a c t i v a t i o n produc ts a re shown i n E x h i b i t s 4 t o 9 f o r a f o r -
ward p e r t u r b a t i o n o f parameters 1 t o 6, r e s p e c t i v e l y . I n cases where t h e
r e s u l t s o f t h e fo rward p e r t u r b a t i o n a n a l y s i s were thought t o p r o v i d e a
poor approx imat ion of t h e l o c a l g rad ien ts , check c a l c u l a t i o n s were per -
formed us ing t h e r e s u l t s o f fo rward and backward p e r t u r b a t i o n runs. For
a l l c a l c u l a t e d normal ized s e n s i t i v i t y c o e f f i c i e n t s , p e r f e c t agreement was
found between GRESS and p e r t u r b a t i o n a n a l y s i s r e s u l t s w i t h maximum d i f -
f erences we1 1 w i t h i n t h e range o f t h e expected p r e c i s i on ob t a i nab1 e f rom
p e r t u r b a t i o n a n a l y s i s us ing r e s u l t s p r i n t e d w i t h s i x s i g n i f i c a n t d i g i t s .
The method o f d e t e r m i n a t i o n o f expected p r e c i s i o n i n t e r v a l s i s o u t l i n e d
i n t h e Appendix.
7 i*Li
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Exh- ib i t 4. S e n s i t i v f t i e s t o parameter 1 approximated f r o m fo rward perturbation a n a l y s i s .
17
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CL 3 5 C L 36 CL 37 CL 38 ti 381: A R 36 P R 3? A R 38 A R 3 9 A R 60 AR 41 AR 42
K 2 9 K 40 K 41 u 62 K 43 K 44
C A 40 C k 4 1 C A 4 2 C A 4 3 C A 44 C A 45 C A 46 C A 47
. C A 48 C A *a sc s5 5C 46 SC 46tl se 47 sc 48 sc 49 SC 50 TI 4 6 7 1 47 71 48 T I 49 T I 50
7 t4UCLlOE TABLE R ~ ~ D I O A C T I V X T Y ~ CURIES PCTIVATION PRODUCTS PERTURBATION 15 A 0.1% I f ! C R E A S E I N PU-239 FISSION
SEN5 ( P 3 )
-1.63938E-01
0;o 0.0 0;o 0.0
0.0 0.0 0-0 0.0 0 . 0
0;0 O * O 0 . 0
N -1
E x h i b i t 6. (Cont'd.)
A C T f y A T I Q N PRODUCTS 7 TfWCLInC ?ADLL R4DIOACfIVITY. C U R I E S P E R Y U R B A Y I O N I5 A 0.1% I P ~ C R E A S E I N Z I Q C A L O Y FLUX
E x k i b i t 7.
0.0
0.0 0.0
0.0 5.036946-03
0.0
0.0 0.G 9.98U78E-08 0.0 l.Y96r9E*00
0.0 0.0 3 . 0 0 2 3 f l E * 0 0 u.0
0.0
0 . 0 0 3 0 a
0.0 0 . 0 1.OOJjSE*r)O 1.99$99€*00 0.0 9.96383E-01 T.9 9-433- 2 . 0 8 o ~ d E * 0 0
0.0 a r c 0.0
FUEL
Dert u r b a t i on
?5fNSaPb,
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 090 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
- 0 . 0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0;0 0 0 0 0.0 0.0 0 eo
0.0
5 . 0
Sensitivities t o parameter 4 approximated f r o m forward , a n a l y s i s .
N N
9.99786E-01 1.99~~?€+00
FUEL SENS ( P h t
0.0 0.0 0 . 0 0.0 0.0 0.0 0.0 0.0 0.0 0 . 0 0.0 0.0 0.0 0.0 0.0 0 . 0 0.0 0.0 0.0 0.0 0.0 0.0 o * o o e o 0b0 0.0 0 ; 0 0 . 0 0 . 0
N w
E x h i b i t 7 . (Cont’d.)
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P t R l ( P S I F U t L P E R T ( P 6 )
E x h i b i t 8. Sensitivities t o parameter 5 approx imated from f o rward perturbat ion a n a l y s i s .
SI 31 SI 32
P 33 P 34
s 34 s 55 S 3b
CL 56
CL 3 8 M Ad 3 b AH 3 7 AU 38 A H 39 A H 40
K 5 9
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T I 4 9 T I 50 r f 4u
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(r 1:!!v099Et00
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29
V. CONCLUSIONS
The GRESS automated procedure was s u c c e s s f u l l y a p p l i e d and v e r i f i e d
on ORIGEMZ, a l a r g e code (more than 5K ca rds ) u s i n g complex cod ing and
r e s o l u t i o n methods t o ca c u l a t e cha in b u i l d u p and decay o f l a r g e numbers
o f n u c l i d e s and elements (more than 1600) i n nuc lea r reac to rs . The
double p r e c i s i o n GRESS 1 b r a r y a l l o w i n g c a l c u l a t i o n o f s e n s i t i v i t i e s f o r
mixed s i n g l e and double p r e c i s i o n v a r i a b l e s was used i n c o n j u n c t i o n w i t h
t h e GRESS precompi le r . A sample problem i n v o l v i n g f u e l kurnup under
s p e c i f i e d power, r a d i o a c t i v e decay, and m a t e r i a l i r r a d i a t i o n under spec i -
f i e d f l u x was used f o r t h e s e n s i t i v i t y c a l c u l a t i o n and v e r i f i c a t i o n
a n a l y s i s . S e n s i t i v i t i e s were c a l c u l a t e d fo r a l l p r i n t e d n u c l i d e concen-
t r a t i o n s (more than 1600) i n two ORIGENZ vec to rs w i t h respec t t o s i x
parameters. The accuracy o f t h e GRESS r e s u l t s was v e r i f i e d u s i n g p e r t u r -
b a t i o n a n a l y s i s methods. Together w i t h p reced ing v a l i d a t i o n s t u d i e s
u s i n g t h e WENT code7 and t h e UCBNE-10.2 code,8 t h i s a n a l y s i s demon-
s t r a t e s the e f f i c i e n c y o f the GRESS automated procedure i n c a l c u l a t i n g
model s e n s i t i v i t i e s and f u r t h e r i l l u s t r a t e s i t s a p p l i c a b i l i t y t o a wide
v a r i e t y o f numer ica l codes.
31
REFERENCES
1. A. 6. C r o f f , "ORIGENZ - A Revised and Updat d Version of t h e Oak Ridge I so tope Generat i on and Dep le t i on Code, I t ORNL-5621.
2. M. J . B e l l , "ORZGEN - The ORNL Iso tope Generation and Dep le t i on Code," ORNL-4628 (May 1973).
3. A. G. C r o f f , M. A. B je rke , G. W. Morrison, and I. M. P e t r i e , "Revised Uranium-Plutonium Cycle PWR and BWR Models f o r t h e ORIGEN Computer Code," ORNL/TM-6051 (September 1978).
4. A. G. C r o f f and M. A. B je rke , " A l t e r n a t i v e Fuel Cycle PWR Models f o r t h e ORIGEN Computer Code," ORNL/JM-7005 (February 1980)
5. A. G. C r o f f , R. L. Haese, and N. B. Gove, "Updated Decay and Photon L i b r a r i e s f o r the ORIGEN Code," OKNL/TM-6055 (February 1979).
6. E. M. Oblow, "GRESS, Gradient-Enhanced Software System, Version D User s Guide, ORNL/TM-9658 ( J u l y 1985).
7. E. M. Oblow, F. G. P in and R. Q. k l r ight , " S e n s i t i v i t y Ana lys i s Using Computer Ca lcu lus : A Nuclear Waste I s o l a t i o n App l i ca t i on , " Nucl, - Sci . Eng, ( I n p ress) .
8. F. G. Pin, R. A. Worley, E. M. Oblow and R, Q. Wright, "An Automated S e n s i t i v i t y Ana lys is Procedure f o r t h e Performance Assessment o f Nuclear Waste I s o l a t i o n Systems," Nucl. Chem. Waste Manag. ( I n press).
I_-
- I__I_
33
APPEND I X
Method o f Determinat ion of P r e c i s i o n I n t e r v a l s
Th is attachment b r e f l y descr ibes a method t o determine expected
p r e c i s i o n i n t e r v a l s whe.. approx imat ing g r a d i e n t s and s e n s i t i v i t i e s f rom
r e s u l t s o f p e r t u r b a t i o n a n a l y s i s p r i n t e d w i t h n s i g n i f i c a n t d i g i t s .
L e t V , F and B be t h e r e s u l t s o f a c a l c u l a t i o n corresponding t o an
unper turbed case, a forward per tu rbed case ( i . e . t h e c a l c u l a t i o n is per-
formed w i t h a p o s i t i v e parameter p e r t u r b a t i o n ) and a backward per tu rbed
case (i.e. t h e c a l c u l a t i o n i s performed w i t h a negat ive parameter p e r t u r -
b a t i o n ) , r e s p e c t i v e l y . Assume t h a t t h e per tu rbed cases i n v o l v e p% p e r t u r -
b a t i o n ( p o s i t i v e o r negat ive) i n t h e va lue of t h e parameters o f i n t e r e s t .
Then,
and F-B 100 sc = - x - v 2 P
represent normal ized s e n s i t i v i t y c o e f f i c i e n t s o f t h e v a r i a b l e 11 w i t h
respec t t o t h e parameter o f i n t e r e s t approximated from forward per tu rba-
t i o n a n a l y s i s and centered ( f o r w a r d and backward) p e r t u r b a t i o n ana lys is ,
r e s p e c t i v e l y , These s e n s i t i v i t y c o e f f i c i e n t s are exact o n l y when t h e
v a r i a b l e V behaves l i n e a r l y i n t h e i n t e r v a l [B, F], Th is i s no t g e n e r a l l y
t h e case and t h e r e f o r e , SF and SC c o n s t i t u t e o n l y approx imat ions o f t h e
s e n s i t i v i t y c o e f f i c i e n t a t t h e s o l u t i o n p o i n t V. I n a m a j o r i t y o f prob-
lems, t h e assumption o f l i n e a r i t y can be made a reasonably c l o s e one i f
34
t h e i n t e r v a l [S, F] i s smal l . Th i s i s g e n e r a l l y achieved by s e l e c t i n g a
smal l va lue o f t h e parameter p e r t u r b a t i o n p.
However, i n a l l cases ( i n c l u d i n g l - i n e a r caws) , due t o t r u n c a t i o n
e r r o r s in t h e p r i n t e d values o f t h e v a r i a b l e s V, F and B , SF and SC a re
c a l c u l a t e d w i t h i n a c e r t a i n e r r o r range which depends on t h e number o f
d i g i t s w i t h which t h e v a r i a b l e s a re p r i n t e d .
Assume t h e r e s u l t s a re p r i n t e d w i t h n s i g n i f i c a n t d i g i t s i n t h e Form
VxEa
BxEb
FxEc
where V, B and F are now n d i g i t s r e a l numbers w i t h decimal p o i n t t o t h e
r i g h t o f t h e f i r s t d i g i t , and Ea = l o a . For smal l p e r t u r b a t i o n s a, h and
c do n o t d i f f e r by more than 1, i.e., I a - b l G 1, I a - c l < 1 a n d l b - c l 4 1.
Then SF and SC are c a l c u l a t e d w i t h i n an e r r o r range such t h a t
FEc-a - V 100 + (5 x 10-n __ (1 -+ Ec-a) 100 ) T S F - (---.-..."
V 1
and + ( ~ . l O - - n (Eb-a d- E c - a l .
2P 1 FEc-a - BEb-a) 100 2P - V sc = (-- 1 V
The e r r o r ranges d e f i n e t h e expected p r e c i s i o n i n t e r v a l s w i t h i n
which SF and SC approximate t h e exact s e n s i t i v i t i e s a t t h @ p o i n t s o l u t i o n
V. The expected p r e c i s i o n i n t e r v a l s can be l a r g e depending on the r e l a -
t i v e values o f a, b, c, n, V and p and should be taken i n t o account when
comparing approximate s e n s i t i v i t i e s such as SF and SC t o exact l o c a l
35
s e n s i t i v i t i e s such as those c a l c u l a t e d by GRESS. This i s e x e m p l i f i e d
b e l ow.
A code such as ORIGENZ c a l c u l a t e s v a r i a b l e s i n s i n g l e p r e c i s i o n ,
hence 6 s i g n i f i c a n t d i g i t s accuracy i s w e l l w i t h i n t h e t r u n c a t i o n e r r o r
range o f t h e c a l c u l a t i o n s . The code, o r i g i n a l l y designed t o p r i n t r e -
s u l t s w i t h 4 s i g n i f i c a n t d i g i t s was m o d i f i e d t o p r i n t 6 s i g n i f i c a n t
d i g i t s . Small parameter p e r t u r b a t i o n values o f 0.1% (p = 0.1) were used.
Assume t h e r e s u l t s o f t h e code are
V = 1.00014 Ea
F = 1.00025 Ea
B = 1.00003 Ea
t h e n t h e va lues o f SF and SC i n t h i s case are:
o r
o r
0.99986 x 10-1 <SF < 1.19983 x lo-'
1.05000 x 10-1 <SC < 1.14984 x 10''
SF = 1.09985 x 10" - t 9.99850 x
SC = 1.09992 x 10" - f 4.99200 x l o m 3
SF = 1.09985 x 10-1 - + 9.1%
SC = 1.09992 x 10-1 I t 4.5%.
Thus, f o r t h i s example, t h e bes t p r e c i s i o n expected on t h e va lues o f
SF and SC a re 9.1% and 4.5% r e s p e c t i v e l y .
I n t h e GRESS s e n s i t i v i t i e s v e r i f i c a t i o n study, expected p r e c i s i o n
i n t e r v a l s were c a l c u l a t e d whenever d i f f e r e n c e s o f more than 1% were ob-
served between t h e GRESS and p e r t u r b a t i o n a n a l y s i s r e s u l t s . I n a l l cases,
GRESS r e s u l t s and p e r t u r b a t i o n a n a l y s i s r e s u l t s agreed w i t h p r e c i s i o n s
much b e t t e r than t h e expected p r e c i s i o n .
37
ORNL/TM-9694 D i s t . Category: UC-70 (Waste)
1-5. 6. 7.
9. 10. 11. 12. 13. 14. 15. 16. 17.
23.
8,
18-22.
INTERNAL DISTRIBUTION
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53. O f f i c e o f A s s i s t a n t Manager f o r Energy Research and Development, DOE-ORO, Oak Ridge, TN 37830
Rockwell Hanford Co., P. 0. Rox 800, Richland, WA 99352
54. R. P. Anantatmula 58. P. #. C l i f t o n 62. B. Sagar 55. H. Babab 59. C. DeFigh-Price 63. J . Sonnicksen 56. M. Bensky 60. C. McLane 64. R. Wi ld 57. L. C. Brown 61. D. O l i v e r 65. D. Wood
B a t t e l l e Memorial I n s t i t u t e , O f f i c e o f Nuclear Waste I s o l a t i o n , 505 K ing Avenue, Columbus, OH 43201
66. A, B r a n d s t e t t e r 67. P, Baybutt 68. W, A. Carbiener 69. N. E. C a r t e r 70. S. K, Gupta 71. W. Harper 72. W. M. Hewi t t
73. 6. Jansen 74. J. F. K i r c h e r 75. E. Meadow 76. J , Parry 77. G. E. Raines 78. R. E, Thomas 79. ONWI L i b r a r y
P a c i f i c Northwest Laboratory , P.O. Box 999, Richland, WA 99352
80. M. Apted 81. C. Cole 82. P. Doctor 83. R, Er ikson
84. M, Foley 85, A. L i e b e t r a u 86, M. Piepho 87. S. Sneider
38
PROSE, Incorporated, 36 Malacja Cove Plaza, S u i t e 309; Palo Verdes Es ta tes , CA 90274
88. M. Robinson 89. R. L. Stark
Sandia Na t iona l Labora to r ies , P.Q. Box 5800, Albuquerque, NM 87185
90. F. W. Bingham 91. R. Cranwell 92. J . C. He l ton 93. N. Hayden 94. R. b. Iman
95. C. D. Leig 96, R. W. Lynch 97. R . Peters 98. S. Sinnock 99, M. Tierney
U.S. DOE - BWIPO, Richland, dA 99352
100. D. H. Dahlem 101. P. E. Lamsnt 102. M. K. Thompson
U.S. Nuclear Regulatory Commission, Washington, D.C. 20555
103. Lee Abramson 109, M. Cunningham 114. J. Linehan 104. L. B a r r e t t 110, M. 3. Gordon 115, M. Logsdon 105. J. Bradbury 111. J . Greeves 116. 1. Margu l i es 106. R. Buchbinder 112. T. Johnson 117. 3. Randal l 107. R. Codel l 113, L e Lancaster 118. D. Rasmuson 108. E. Cont i
119. Donald Alexander, U.S. DOE, C i v i l i a n Rad ioac t i ve Waste Management Program, 1000 Independent Ave., SW, Washingtan, O.C. 20585
120. C. Kop l i k , The A n a l y t i c Sciences Corporat ion, 1 Jacob Way, Reading, Massachusetts 10867
121. W. J. Kurzeka, M y . , Commercial Naste Tech. U n i t , Rockwell Hanfard Operat ions, P.O. Box 800, Richland, WA 99352
122. 0. Langmui r, Dept. o f Chemistry and Geochemistry, Colorado School o f Mines, Golden, CO 80401
123. W. L. Lee, R. F. Wcston, Inc., 2301 Research Blvd., R o c k v i l l e , MD 20850
124. J. A. Lieberman, OTHA, Inc,, P.O. Box 651, Glen Echo, MD 20812
125. J. 0. Neff , U.S. Dept. o f Energy, R ich land Operat ions O f f i c e Columbus, 505 King Avenue, Columbus, OH 43201
126. T. H. Pigford, Dept. of Nuclear Engineer ing, U n i v e r s i t y OF C a l i f o r n i a , Berkeley, CA 94720
127. J . Rhoderick, U.S. UOE/OCRW#, 1000 Independence Ave., SW,
128-432. For d i s t r i b u t i o n as shown i n TID-4500, D i s t r i b u t i o n category UC-90 - Nuclear Waste Management