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3 445k 0349493 9 ok

 

HEAVY ISOTOPE BUILD-UP IN CORE

233

OF U BREEDER

 

J. Halperin and R. W. Stoughton

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OAK RIDGE NATIONAL LABORATORY
OPERATED BY
CARBIDE AND CARBON CHEMICALS COMPANY

A DIVISION OF UNION CARBIDE AND CARBON CORPORATION

POST OFFICE BOX P
OAK RIDGE. TENNESSEE

   
 

 

This document consists of 26 pages

® Copy ?‘ of 176 coples Series A

Contract No W-T405-eng-26

CHEMISTRY DIVISION

HEAVY ISOTOFE BUILD-UP IN CORE OF U233 BREEDER

J Halperin and R W Stoughton

DATE ISSUED

0CT 6 1953

swrrmcnnsrs DEGLASSIFIED

By AUTHORITA%%Q_ mé il & :zt~ - .

VLY
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A Divasion of Union Carbide and Carbon Corporation
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iv # 75

o,

Heavy Isotope Burld-Up In Core of U233 Breeder

Je Halperin and R. W. Stoughton

Abstract

The build-up of uramium i1sotopes with time in a U233 breeder core
was calculated for five different cases, the difference depending on the
startang fuel and the 1sotopic composition of the continuously added
make-up fuele The total uranium concentration was found to approach
slowly an equilibrium value of 2.6 to 3.5 times the starting value,
depending on the composition of the make-up fuel. In all cases the net
neutron losses per net neutron reproduced in the core go through a
maximum of less than 1% at a flux-tame of about 3 x 1021, go through a
mimmm of about -~0,6% (1.€. a net gain) at about a flux-time of
L x 1022 s and approach equilibrium values of about 0.3% at flux-times

above 6 x 1023.

sy

 
k : Y

o ] =

The principle heavy i1sotopes in the core of a U233 breeder reactor and their
modes of formataion may be depicted by the following diagrame

ye33 &Efllfil; ye3b .£§£E1> 235 _iEzlE)> U236 .LE;I1> 237

(n, fiss,) (n, fiss,) P- 16,7 day

The production of these species as well as of several other heavy muclides i1n

the core of a breeder starting with pure U233 has been discussed by'vlsner(l)

 

(1) 8 Vaisner, ORNL-CE No. 51-10-110 (0Oct. 1951).

 

and by Halperin and Stoughton(la)o Both the growth of the various isotopes and

 

(la) J. Halperin and R W, Stoughton, ORNL-1368 (Sept. 1952),

 

the net effect on neutron economy were presented 1In this paper five cases will
be considered with more recent values for the various cross-sections
I Pure U233 in core at start, pure U233 added to core,
ITo Pure U%33 in core at start, y233 containing 5% 23l added to core as
the fuel 1s consumed,
ITI. U233 containing 5% U23h in core at start and added to core.
IVe Pure U235 in core at start, pure U233 added to core.
Ve Pure U235 in core at start, ye33 containing 5% p23l added to core,
In any practical case the core will probably start with U235 *. As this
material 1s consumed U235 will be added at first, and then very soon the added
material should consist of the U233 product produced in the blanket. Some U23h

will be produced in the blanket by neutron capture of the members of the 233

 

O

¥ Actually this starting material will contain about 1,0% U23h, 93¢ 235 and 6%
U238° The U23h and U238 wLll increase the losses over those calculated in this
paper for Cases IV and V at the shorter times, the magnitude of this additional
loss will be about 0,174 at zero time and 1t will steadily decrease with

increasing time.

 
o'

-2 -
chain (Th233, Pa233 and U233) and 1t 15 felt that an upper limit on the U23h/U233
ratio for the blanket product will be about 0.05 1f the overall losses are to
be kept wathin reason. Hence any practical case 1s expected to lie somewhere
in between Cases IV and V Cases I, IT and ITI are included for comparison and
because some future reactors may actually start with U233 1n the core The
effect of U237 wall not be considered because 1t 18 expected to be destroyed
predominantly by beta decay and 1ts cross-sections are not known, Its concen-
trations and possible effects have been considered in a previous paper(l)

For Case I the concentration of U233 1s considered constant. Actually its
concentration will increase somewhat as various pile poisons (e.ge fission products,
U23h etc.) grow 1n and 1ts concentration may then decrease somewhat in the core
as 1t increases in the blanket. If the core and blanket are processed
contimiously, however, these effects will reach a steady state value rather soon,
if they are processed batchwise, then the tame average value will be constant
from period to period. The effect of the heavy i1sotope build-up 1tself on
required U233 concentration changes 1s small as will be seen from the small effect
of this build-up on neutron economy,

The values of the various cross-sections used here are gaven in Table 1.

Table 1,

Thermal Cross-Sections and Eta Values

 

 

 

Nuclade 6 ca
y?33 50 56l
g2 90 90
y235 106 682
7236 8 8
Mo = 2,12 Moj = 2.30

 
-3 -
Case I+ Pure U233 In Core at Start, Pure U233 added.

The differential equations for the three changing species are

an
_£E= Np3E §o(23) = Ny f S(2h) (1)

dN
"&’ii N f O, (2h) = Nyef G, (25) (2)

aw
_fii Npef O(25) = Nogf Go(26) (3)

Here the N's indicate concentrations, G, and O ; indicate cross-sections for
neutron capture and absorption (1.e. capture plus fission) respectively, and the
two-figure index numbers indicate the last figure of the atomic number and last
figure of the atomic mass respectively for the nuclide in question, The relataive
concentrations of the heavy i1sotopes at equilibrium are obtained by equating the

differential equations to zero, thus

 

N2y, 60(23) 50

—_—= = = 00556
Npg G, (2L) 90

N25 60(23) 50

N_2; = m = 587 = 0,073
Nog  0.(25) 0c(23) 106 x50 4 om
Nog T C,(26) 0, (25) =8 x 682 ~

 

1,600

1

Adding umity for the U233 1tself, the ratio of total uramum to U233 at equilibrium

becomes 2,60,

Integrating Equations (1), (2) and (3) the time dependent isotopic ratios

become
N -0 . (2L)ft
—g-li.: a(l-e c(2h) ) (L)

 
-1 -
23
where a) - O-\_C(._l = 0,555 555 555 6

 

 

 

 

S e(2h)
Nos . _GL(2L)ft -G
N_z.; = ag * bge c(2L)ft ce a(25)ft (5)
wh . 0c(23) _
ere ag ) T 0o 782 99
b - 0c(®) - -0.08L L59 L59 L6
03(25) - Gc(zh)
g = O(23) 0o (2h) = 0,011 145 676 L6
G (25)[C,(25) - & (2]
N
N_z_g . bée_G‘c(zh)ft+ g a(25)ft | dée..@c(26)ft (6)
where a; = 0\6(‘___‘2’235) = 06971 LOT7 62k 6
C
bg = "5 Oc(25) _ 0,109 179 30L 2
G ,(2h) =~ C°-(26)
cg = 25 %(%) - -0,00L 752 880 868

63(25) - 63(26)
d6 = -(a.6 + bg + cg) = ~1.078 83L OLL 9

The net neutron loss per fuel atom destroyed in the core is then

Mol Oo(®) | 0 gy M25 Tal25) | Wag Tc(26)

 

L(23), =

 

The net loss per net neutron reproduced in the core 1s
1(23)o/(MN23 = 1)
where ‘Q 23 18 the neutrons produced per neutron absorbed by U233. The subscript

zero indicates no 1}23)'t in the U233 added to the core,

Case II Pure U233 In Core at Start, U233 Containing 5% U23h Added.

The contribution to each 1isotope (U23h, U235 and U236) 1s divaded into two

 
=5 -
parts (1) that resulting from the U233 originally present and the y233 added
to the core, N;, and (2) that resulting from the y23h added wath the 0233, the
N: contribution, The first part Nl in each case 1s Just that calculated in
gase Io The second part in each case N: 1s proportional to Ni. Thais can easily
be seen as follows,
Remembering that U233 (from the blanket) 1s added at the same rate that it

is destroyed in the core

-EE- = production = destruction
Li§
= riN,3f G,(23) - Ny £ O (2h)
where r = N2h/N23 ratio in the blanket product, this product

1s added to the core as needede.
Thus this equation 1s simlar to Equation (1) except that 6‘&(23) an Equation (1)

1s here replaced by rG,(23)s The solutaon then is

By TOLCY O, T Ny,
— T cmmmm——icusms - e £ ———— —
Npq Gc(fll) 0.(23) Noj

The total U23h 1s given by

Nay Nl Np) [1 rG‘a(ZB)] N,

 

 

8
N3 Nz3 N3 Se(23) | Wa3 ®)
where Néh/NZB in Case II 1s equal to Nzh/N23 calculated an Gase o
Similarly the total of each of the other 1sotopes is given by
r Y
No r&.(23) | N
23 + c No3
N I r6,(23) 1 N
.2,6.. =1 + ___a_'(__.... ..3..6, (10)
N23 I O’(;(23) N23

 

1
where the primed N2h’ NES and Néé here are equal respectively to N2h’ NZS and Nog

1n Equations (L), (5) and (6).

 
- 6 -
The net loss per net neutron reproduced in the core becomes

L(23)r r o, (23) L(23)o
={1=+ “ 5
s -1 G, (23) ‘023 -1

where L(23)0 1s given by Equation (7). Thus each 1sotopic ratio and the net loss

 

(11)

 

in Case IT 1s equal to [l-r rc‘a(23)/c‘c(23)] times the same quantity for Case I,

The value taken for r is 0,05 (1.e 5%).

CasellI U233 Containing 5% 1123h In Core At Start And Added To Core.

 

This case will be the same as Case II except for the added contribution to
the U23h, U235 and U236 resulting from the U23h originally present in the core,
This contribution 1s calculated for each i1sotope and added to the results in
Case II.

Lettang Ngh = original concentration of U23h

N'g = concentration of this U23,4 left at any time,

Nap NS
—2h . T2 -G (2b)rt - 6, (2L)5t

= 0,05 e
Np3 N3

Using this equation and solvang equations lake (2) and (3), the U235 and II236

#*
contributions, Nog and N'Eé are obtained

N3 _ oo(2h) N3), (o~ Tel)TE _ -0, (25)1t
No3  (G,(25) = Go(2h) Ny

= 0,00760135 (e~ Oc(2b)ft _ -Ga(25)fty

N§6 O (2h) 5 (25) N, [~ 0 ,(25)ft o= Oc(2h)ft +
No3  (Ca(25) = G, (2L)) Np3 [ O,(25) = O (26) O ,(2k) =G (26)

 

)

 

( 1 ] 1 o 0'0(26)ftJ
G,(2h) =G (26) ~ T,(25) -~0,(26)

O, (25)ft

= 050239093 &~ - 0,296523 &~ P2t 4 0172613 o= Oc(26)2t,

 
-7 -

The total concentrations of each isotope then become respectively,

N N
2 (Bq. (8)) ¢ 22
23 N23
N25 Nfig
N23 (EQO (9)) * N23
N26 N56
o (1 + 35
T, (B (1) 5o

The contribution to the loss term due to the Ni is

L¥*(23) 1 [y, o) N25 Ca(25) | Wpg O(26)
'Q 23 = 1 Y]23 -1 N23 0" (23) n25 O" (23) N23 0-3(23)

and the total loss per net neutron reproduced in the core becomes

 

 

 

L(23) 1*(23)
——x E o ll +»
To5-1 (Eq. (11)) o3~

Case IV  Pure U235 In Core At Start, Pure 7233 pdded.

 

In this case none of the four isotopes has a constant concentration., As
the original 1235 15 consumed U233 is added and a2 relation must be assumed
between these two species, The assumption made here is that 0233 15 added at
such a rate that the net neutrons reproduced in the core fuel i1s kept constant,

le€o m

(Mg = LIN350(25) = (Mog = LNpg03(25) + (Va3 = L)Np30,(23)

N25 (WZB -1) N23 O, (23) N25 N23
= 3
W35 (Mgs - 1) 15 0a(B) W Wi

where k =,Cra(25) (1125 - 1) .
0_3(23) (”23 = 1)

 

(12)

 

Here the triple prime indicates any isotope resulting from the original UZBS,
the single prime indicates any isotope growing from the added U233, and Ngs indicates

the original U235 concentration. The restriction between Ngs, Ng; and NéB

 
-8 =
could just as well have been made on a neutron reproduction basis (1.e. keeping
N;é T[25 0,(25) + Né3fl23 O'a(23) constant), Using such a different basis would
not have sigmificantly altered the net losses due to the heavy 1sotope burld-up
as calculated here except for the different factor in the denominator depending
on the different basis,
The fraction of the original amount of U235 remaining at any time i1s given

by the expression n

N25 - O’a(gg)ft (13)

0

N25

Using Equation (13) and the differential equation
"y

dlNog

dt

 

ne "
= Nogf O (25) = N, f O(26)
the expression for the U236 resulting from the oraginal U235 becomes

"e
N26 _ 0 ,(25) [e-o'c(zé)ft e o;(zs)ftJ (1L)

N3y O,(25) = O7,(26)
1
The amounts of the various isotopes NEB, N;h, NES and Nog resultang from the

%33 added will now be considered, Combining Equations (12) and (13)

N
23 . (1 - &~ Oal2S)ty 15)

. (Mag - 1) 0(25)
(Mo3 = 1) O3(23)

The differential equations for the other i1sotopes are the same as

 

where k = 1,041 789 L1

Equations (1), (2) and (3) wath each concentration term being primed, Using

these and Equation (15) and integrating

g%—l-‘r- - a,l[l + o e ~Te)b, o e'o'a(zs)ft] (16)
25
' O‘c(23)

where 3 = 6-0_@5 = 0,578 771 894 5

 
-9 -

 

 

 

o O - - 1,152 027 027
L= " 25 - o)
o(2h) = 0,152 027 027
O’a(25) - 0"36210 °
11(2,_5 = ag I:l + b; e-O'c(2h)ft + c% e-O";l(25)ft + d; fte O;(25)ftJ (17)
Nog
' 23
where ag = k %g% = 0,076 377 522 63
2
b; = o (0‘3(25)) = = 1327 166 271

(07a(25) = 0%, (2L))?
o _[(0a(25))° )
(07, (25) = O (21))?

4 - Cc()O0%(5) 103,682 132 L barns
0°,(25) = G o(2L)

 

1| = 0,327 166 271

, ' ? - 25)ft L I
_Ifg_é_ = ag aé + bée-O"c(zh)ft* cée“ O, (25)ft défte Oa(25) + gge o-c(zé)ft} (18)

 

N25
where a.; 18 given above
ag = %% = 13,250 000 000
by = ~b50(25) = 1,715 605 178
6~ 0 (2h) = O 4(26)
1 1
oy = 225 0cl2) 95 9(2) - - 0,075 616 53k 0

 

 

O _(25) - O,(26) (O,(25) - G(26))2

! - 4;0‘;(25) = = 16,306 139 212 6 barns
6~ &7 (25) - O,(26)

 

gy = = (ag + bg + c6) = - 14,889 958 6Ll 00
The total U233 and 23l are given by Equations (15) and (16), respectively,

The total U235 1s given by the sum of Equations (13) and (17), 1.€e,

 
N fry Nl

25 _Yag Mg
O o el
Npz N3z Ng

and the total y236 1s given by the sum of Equations (1L) and (18).

 

o5 _ Mo | Mag
W Nog N3g '
The loss then per net neutron reproduced in the core fuel in Case IV 1is
given by
L(25), _ Np), O%(2k) 1 _ Nag . Nog O(26) 1 } Nog Oo(26) 1
Mos -1 W35 05(25) (Nog -1) N3y N3x T(25) Vipg - 1| W3y O5(25) (Vg -1)

 

 

 

L'(25), 1"'(25),
Nag-1 Mpg -1

Here the single prime indicates contraibution from neutron reactions on the U233

 

(19)

added, the subscript zero indicates r = o; 1.e. that pure 7233 15 added to the core,
The reason for divading these losses into two components will become apparent in

the dascussion of Case V.

Case V U235 In Core At Start, U233 Containing 5% U23h Added.
Here there are three contributions to some of the 1sotopes (1) that

;' part, (2) that resulting from peutron

resulting from the original U235, the N
reactions on the U233 added, the N. part, and (3) that resultang from the y23l
added with the U233, the N; parte The contributions (1) and (2) have already
been evaluated in Case IVe Item (3) will now be considered and then added to
the other two. For this contribution 1t 15 necessary to know the rate of
addition of U932 and not Just 1ts concentration which 1s fixed by Equation (12),

Using Equation (13) and differentiating Equation (12) gives the net rate of
change of y233

! te
dNo3 dN25 "
e T ETa T st ()

But 0233 is destroyed at the rate of N;3f<3;(23). Hence the total rate of
addition of U233 is
KNpEE O, (25) + Np3f 03(23)
since the net rate of change of U233 = rate of addition - rate of destruction.
The rate of addaition of U23h 1s r times the rate of addition of U233 (where r
1s the U23}"/Uz33 ratio in the blanket product)es Using Equation (12) wath the
above expression for the total rate of adding U233 the rate of addition of
U23’4 becomes
kN3t G (25) = Hp3f(07,(25) - 03(23))
and the net rate of change of this contribution to the total U23h becomes
v,
dt

 

= r%ugsf C,(25) - NEBf(G‘a(ZS) - o*a(23))] - N;hf 0. (2k) (20)

The first term in the brackets 1s a constant and the second one varies as Né3.
As will be seen, the calculations may be somewhat simplified if Equation (20)
1s broken up into two equations, one involvaing the constant production term and
the other a negative variable "production" term. Let
= (py)g + ()
Noy = Woplg + Wollys

where the subscripts € and V indicate constant and variable terms, respectively.

Then ( " )
d NZh N
— = = 3L 0, (25) - (Wg))gf O (2h) (208)
d(Ngh)V '
= ~Hlp3T(0(25) - 0% (3))— (Nap)yf O (2k) (20b)

Equation (20a) 1s similar to Equation (1) in Case I where Np3 15 held constant,

 

 
- 12 =
Equation (20b) 1s simlar to Equation (1) wath Né3 being given by Equation (15).
Equations sumilar to (2) and (3) can be written for (Ngg)c, (N;S)V, (Ngé)c and
(Ngé)vp The total solutaon for Ngh will then be a superposition of the solution
given by Equation (L) and that given by Equation (16), that for Ngs, a super-
position of the solutions given by Equations (5) and (17), that for Ngé, a
superposition of the solutions given by Equations {6) and (18). The contribution
to the loss term of the effects of Ngh, Ngs and Nn

2
position of L(23) given by Equation (7) and the Ls(25) part of BEquation (19).

6 will likewise be a super=

Since the solution to the differentaal equation

 

SE Kl(l -e t) = KoNy where Kl’ K, and a are arbitrary constants,
=Kot -at
1s N = Kl -+ ae _ Koe ),
K2 K2"‘a K2 = a

\

1t 1s clear that the solution of the differential equation differing only from
the above by a multiplicative constant in Ky will differ in 1ts solution from

the above by thas same multaplicataive constant in Ky. The coefficients of the
superposed solutions are simply the ratios of the coefficients to N, and

N, (1 - e-CYa(25)ft) 1n the "production"™ terms in Equations (20a) and (20b) to

those in Equation (1) wath Noq being constant and with Np3 being given by

Equation (15), respectavely. Thus

 

 

 

 

 

 

 

 

 

 

 

 

(o)) "N ’ (Nay,) N, ]

ih C = A —g")-!" (EQo (,-l-)) ih v = B .ih.. (qu (16) (21)
Nag | N23 ] N3g N3¢ 1
(Noe) "N (Nao) ! ]

2% _ 4| —25_ (mq. (5)) 27 _ 5|2 (Ra. (7) (22)
Nag | N3 . N3g [ -
(N“ ) T N (N“ ) N -

<2>6 C _ a2 (%q. (6)) -—59-‘-’- = B( 26 (Eq. (18) (23)
o5 L M3 : N5 [Nz ,

where 4 = TXSa(25) _ 0.710800, where = —T(Ta(25) = 0a(23)) . _ 4,118000
O(23) T .(23)

A
 

—]-3-
And for each of the three 1sotopes

N () (M)
= + 2,4
W T WG | g =

 

The total concentration of each 1sotope is then obtained by adding all the
various contributions. The total U°32 1s given by Equation (15). The total

concentrations of the other i1sotopes are
fl

N
-§E [21; (Eqe. (16))J [ 5 (Eqots (21) and (2h)] (25)
N2

N2g |N2g
nt -t B
Nog [N_zi ] Ny } [N 26 }
—=2 - (Bqo (13))|+|=5% (Eae (17))]+ (Eqe's (22) and (2L)) (26)
35 [Nog H“z’s N3s
Nos _[Nog N26 N6
cha : [NOS (Eq. (lh))l "g; (Eq. (18))] [35 (Eqets (23) and (2h))} (27)

 

The total neutron loss per net neutron reproduced in the core fuel is

L(25). [L(25), A [L(23), L, (25),
= (Eq. (19))) + - 731 Eqe (7))]* B *r-“——i-(See EQ. (19))]

 

 

 

 

Tog =1 [Neg-1 25 =
A ro,(25) -r(0,(25) - O, (23))
where - 0_0(23) 0682000 and B AEE)) 0611800

Tt should be noted that the losses calculated on the basis of Ngg, O“a(25)
and (-st - 1) are equivalent to those calculated on the basis of N2°§, O‘a(23)
and (1123 - 1) since
N850, (25) (Mag = 1) = No305(23) (Mg -
or N23 = ng

Obviously the constant, N23, in the Case I, IT, and III are equal to N;B in the
Cases of IV and Vo
Figures 1, 2, 3 and L show the total relative concentrations of each

1sotope and the total losses in each of the five cases considereds From the
- 1l -
way the calculations were made the followang conditions concerming the total
amount of each 1sotope present and the losses should hold after final equilibrium

in reached

 

 

 

(1) Eg& (case I) =Ԥ%- (Case 1IV)
No3 N2g
L(23), L(25),
(2) fi;;:-]-_ (Case I) =‘Q25-]_ (Case IV)
kN, Ny KN,
(3) .I:I;; (CaseTI) = -N?S (Case V) = 'fi;‘; (Case III)
(1) L(23)r (Case II) = fffflE (Case V) = L(23)r (Case IIT)
'fl23-1 Mg -1 To3-1

From the figures these conditions are seen to be satisfied.

A summary of the maxamum losses (all at about ft = 3 x 1021), the minimum
losses (all at about ft = L x 1022) and the equilibrium losses (attained at
about ft = 6 x 1023) are presented in Table 2, In the last column of Table 2
are presented the ratios of the total uramum to U233 at equilibrium, these
values are 2,60 1f pure U233 15 added to the core as fuel 1s burned and 3.50
1f 723 containing 5% U234 15 added, Since these two values probably represent
the two extremes (within the accuracy of the cross~-sections andY| values used)
the most likely value may be about 3,0, Depending on the concentration ranges
being considered, this increase in total uranium could cause increased corrosion
rates or solubility troubles. In aqueous homogeneous U233 breeder reactors
the uramium concentration ranges anticipated (a few grams per liter) are low
enough so that a three-fold increase probably will not cause any appreciable
harm,

The losses presented 1n Fig. 4 are instantaneous values at any gaven ft.

 
- 15 =
The integrated average losses up to any ft value in question are presented in
Fige 5 for Cases I and III, as mentioned previously these two cases probably
represent extremes between which any practical case will lie. The integrated
losses are negative (showing a small net neutron gain): between ft values of
about 2 x 10°2 and 5 x 1023, For a reactor with a core flux of about 1.5 x 1015
and with a total fuel hold-up (in core,heat exchanger, chemical processing, etco)
of 44 or & times that in the core, an ft of 1022 corresponds to about one yearts
operation. Hence for such a reactor the integrated net effect of the heavy
1sotope build-up 1s to cause a small neutron gain from about the second to the

fiftieth year of operation,

 
 

Summary of Losses and Increase In Total Uranium Concentration.

\

Table 2

 

 

 

 

Max, Loss Min, Loss Eq. Loss %—q
Value | Value | Value U
Case In Core At Start Added to Core m % At £t m 9 ft in % | £t above Egq. Value
I pure (233 pure 233 0055 3 x 104 ~e56 |L x 1022 0,25 6 x 1023 2,60
II | pure y233 (U234/y233y = 0,05 | 87 (3 x202 | -.86 |L x10%2 | .38 | 6 x1023 | 3,50
x| (u234/233) = 0,05 | (uPLA?B3) 2 0,05 | W90 |2x 102 | 476 (3x10%22 | 38 | 6x1023 | 3,5
N
- g
v | y23b pure 7233 063 | L x210%L | 45 |4 x1022 | .25 | 6 x1023 | 2,60
v | u235 (w23l/g233y - 0,05 | .89 | L x10%t | -.76 |L %1022 | .38 | 6 x10%3 | 350

 

 

 

 

 

 

 

 

 

 
-17 -

aR—
DWG 19894
VOO —T T TITTITT" T TTIIT 1 T VT T T T T T T T T T 1T

 

 
 
  
 
 
  
 
 

150

—— ISOTOPE BUILD UP WITH FUEL
' 40 REPLENISHMENT OF PURE U233

-—-- ISOTOPE BUILD UP WITH FUEL
REPLENISHMENT OF U233
CONTAINING 5/ U2

130

120

 

 

050+

040+

030

020

 

 

 

R | IIIIIH' RN

102 103 10 10° 10°
10 1

URANIUM ISOTOPE BUILDUP IN CORE OF REACTOR STARTING WITH PURE UR33(ie N2z )

AND REPLENISHING FUEL WITH PURE U%> AND WITH UZ>3GONTAINING 5/ U234 23

 

 

oLt il
10

FIGURE 1

 
-18 -

—
DWG 19891
V0 r—TTT7TITT T T VI T T T 1 T T T LI 1 T T

150 — i -
/
—— STARTING MATERIAL AND FUEL ,

t40= REPLENISHMENT WITH PURE U233 /

130~ ---- STARTING MATERIAL AND FUEL j _
REPLENISHMENT WITH U i
1 20 CONTAINING 5/ U®>? ; B

 

   
  

 

1 00
\23

090

N
—'0807
23
070 —

060

 

050
040
0301
020}

o{O}p~  _.-- 7 e -ggp——-— = m-—-——--o

000l 1 L LLLLI ool

{ 10 102 103 104 105 10°

 

 

 

 

  

 

10714
URANIUM ISOTOPE BUILDUP IN CORE OF REACTOR STARTING WITH PURE U* (ie %"'—4 0)

23
AND REPLENISHING SPENT FUEL WITH PURE U?*> AND STARTING WITH u?*®
CONTAINING 5/ U?** AND REPLENISHING THE SPENT FUEL WITH URANIUM
OF THE SAME GOMPOSITION

FIGURE 2
-19 -

160 DWG 19893
T TTITI T T TTTIT]

 

150
———— FUEL REPLENISHMENT
1 40— WITH PURE U%%

--—— FUEL REPLENISHMENT

WITH U CONTAINING 57 U

234

120

 

1 Q0=
Q90—

— 080

Nos 23
Q70

060

 

0501 J
0 40— /
030f /

0 20— J/

 

 

 

 

| 1 11 — -1 | |||.- L L | L bl
0 2 3 4 5
1 10 10 10 10 10 10
10 21t
URANIUM ISOTOPE BUILDUP IN CORE OF REACTOR STARTING WITH U235 AND

REPLENISHING FUEL WITH PURE U233 (1e 2% 0) AND WITH U233 CONTAINING 5/ U23*
23

 

FIGURE 3

 
 

-~

Is

J 3

—

DWG 49892

 

 

0 96 i IIIHHI { FIIiHI, i llllllll [ IIIIHW | IIIIIIII t T T TTTT
- {25) N {26)
S L(23) 1 [ Nag o (29 Nas 267
084 s / \\ Moz b Tpy ! [Nza czm s Npzo (23] Nyyo (23)
/ \
072 - - ,, ‘\ L{25) | Npac (24) Nas  Npgo {26)
- J ‘\ Tos | [Npso (25)(mpg 1) Npg  Npso (25)(m,5 1)
0 60F J %
/ W
/ \\
048 / W —
/ o
036 / \ —
;S / /
024 /7
/
012 - i 7
e _ - \ 1Y
0 QQpmesee==" oo ——— 7 \ ~
0 12 I STARTING WITH u2® 4 -
—— A REPLENISH SPENT FUEL WITH
0241 PURE U233 ‘\ -
- B REPLENISH SPENT FUEL WITH i
0 36k U233 GCONTAINING 5/ U239 \\ _
II STARTING WITH U233CONTAINING \\
048 — — 5/ U234 AND REPLENISHING \} _
SPENT FUEL WITH URANIUM OF \
0 60 L THE SAME COMPOSITION /
I STARTING WITH PURE U235 I’ LOSSES PER NET NEUTRON
0 72 ——== A REPLENISH SPENT FUEL WITH v /! REPRODUGED _
PURE U233 \ > /IN CORE (") LOSSES PER
1
0ogalL B RIéZ%LENISH SPENT FUEL WITH v/ FUEL ATOM DESTROYED- (5 1)
U=°° CONTAINING 5/ U234
0 96 Pt Lt | IIIIIII| | IHI!I!I ] IllIIH| Pob i

 

 

     

 

 

LOSSES PER NET NEUTRON REPRODUCED IN CORE DUE TO GROWTH OF URANIUM ISOTOPES

10 102
10

103

19

ft

104 103 106

FIGURE 4

Xty

_Oz_
 

S
DWG 20513

 

+ 100 T T T T T T T T TTTT T T T T T — T T T TTTT
O S0 —— STARTING WITH PURE U233~
0 80L N AND REPLENISHING _

rad \ SPENT FUEL WITH PURE U233
- - \ -
070 -7 \ ——— STARTING WITH U233
ogoFE——————""7"~ \ CONTAINING 54 UZ>* AND
\ REPLENISHING SPENT FUEL
050} WITH URANIUM OF THIS SAME

 

_050 1 1 lllllll

| lIlIlII

] IlIIll!l

 

llllllll 1 Illlllll 1 (RN

COMPOSITION

 

 

 

 

 

1073 1072 1o~ 1 o . 102 10°
TIME (in years at average flux of ~ 3 x 10 ')
1 1 Iilllll 1 1 lllllll 1 | IIIIHI I | IIIIIII | 1 IIIIlI| 1 1 L1 1101
1 10 102 103 104 109 108
107" 11
FIGURE 5

INTEGRATED LOSSES AS A FUNCTION OF FLUX-TIME

_lz_
-22 =

Acknowledgement

 

The authors happily acknowledge the helpful advice and criticism of

R A Charpie during the preparation of this report,

&