.
.
.
:
La
.
:
| OF |
ORNL P
2555
.
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.
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--
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to
.
EEEFEFEE
1:25 11.4 116
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
ORNAD-2556...
ORNL - AEC - OFFICIAL
MASTER
NOV 2.9 1968
#ga 100 56
Conf. 661011-6
ORNI - AEC - OFFICIAL

:: EYPERIENCE IN COMPUTING RESEARCH REACTOR FUEL BURNUP
CONTRASTED WITH RECOVERY RESULTS*
T. P. Hamrick and H. F, Stringfield
Oak Ridge National Laboratory
Oak Ridge, Tennessee
ABSTRACT
For several years ORNL has operated reactors for research purposes which
utilize highly enriched uranium as fuel. In accordance with AEC nuclear
material management procedures, it has been necessary to calculate fuel losses
by burnup for material balance purposes. This paper deals with the methods used
in computing burnup including the formulas, the source of errors, and the adjust-
ments in the formulas required to minimize errors. In addition, the amount of
fuel calculated to be contained in the several hundred fuel elements that have
been sent for recovery ls compared with the reported recovery results.
Introduction
Consuming a fissionable material in a nuclear reactor is a process that is
well understood, and good analytical models are available for the solution of
this process. However, when these models are applied to an actual reactor,
difficulties are a lways encountered. For several years, Oak Ridge National
Laboratory (ORNL) has operated light-water-moderated-research-reactors which
utilize highly enriched uranium as fuel.
It was known from the beginning that some sort of estimate of the amount
of fuel consumed must be made to satisfy the Atomic Energy Commission (AEC)
requirements of fissionable material accountability. Later, as technology
developed and reactor power levels became higher, it became evident that not
only the amount of fuel consumed was important, but w
sumed. Primarily this was due to the following reason. In the low power reactor,
the element life was determined not by burnup but by corrosion so that cores were
replaced in entirety and the residual uranium was recovered by processing the
core as a unit. This method is still used in many low power reactors whereby
*Research sponsored by the U. S. Atomic Energy Commission under contract with
the Union Carbide Corporation,
LEGAL NOTICE
ORNI - AEC - OFFICIAL
ORNI - AEC - OFFICIAL

RELEASED FOR ANNOUNCEMENT
This report was prepared as an account of Government sponsored work. Neither the United
States, nor the Commission, nor any person acting on behalf of the Commission:
A.Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, mathod, or process disclosed in this report may not Infringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, method, or process disclosed in this report,
As used in the above, person acting on behalf of the Commission" includes any em-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to, any Information pursuant to his employment or contract
with the Commission, or his employment with such contractor.
IR NUCLEAR SCIENCE ABSTRACTS
the amount of fuel consumed is evenly distributed to the elements which make up
the core. Upon the advent of higher power reactors, the element life became ,
shorter and the primary reason for reprocessing an element was due to the low
amount of residual fuel instead of corrosion considerations. Then the cores
were not processed in entirety and the residual uranium was recovered by pro-
cessing individual or specific groups of elements, some of which had been in
many core loadings. This added consideration made it necessary to know where
the residual uranium was located in order to know which eludent to reinsert
into the core to optimize the fuel element cycle while keeping in mind the
economic implications.
ONNI - AEC - OFFICIAL
Burnup Calculation
One of the first position-type burnup calculations for highly enriched
uranium was initiated in 1952 to be used for the Low Intensity Test Reactor.
(LI'IR). It consisted of the following:
The assumption was made that the burnup rate is 1.26 grams
per MWD. Of this quantity, 1.07 grams undergo fission and
0.19 grams was converted to 2360. Therefore, the total burn-
up for a core was the power level times the number of days
operated at this power level multiplied by 1.26 which resulted
in the total fuel couis umption.
This total fuel consumption was then distributed among the
several fuel elements and fuel follower shim rods in the core.
during that particular run. This distribution depended upon
the average thermal neutron flux per fuel element. In order
to make the calculation of thw fraction of the total burnup
that should be assigned to any element easy, the sum of the
burnup factors for all core positions should be unity.
* Determination of Burnup Factor I
.
According to the above description, the fraction of the total burnup
which occurred in position i would be
Burnup in 1. = gi
Burnup in core
where
was determined from a flux map
It was recognized that the above conditions held only for a short time but was
assumed to be reasonable since as $. changes, 0 also changes proportionally.
Each burnup factor was adjusted so that the sum would be unity by dividing each
factor by the sum of the factors.
ORNL - AEC - OFFICIAL
23-
For our study of the "Evolution of Burnup Factors", let us assume a
hypothetical core such as the following:
OINI - AEC - OFFICIAL
1
2
3
4
5

EBF Core
Core Statistics
235u (grams)
Core Position
Fuel Type
BUF-I
A-1
200
180
Fuel
Fuel
Fuel
Fuel
Fuel
A-2
A-3
A-
A-5
160
0.833
0.952
1.071
0.892
0.773
0.05553
0,06347
0.07141
0.05947
0.05153
180
200
Fuel
Shim Rod
B-1
B-2
B-3
B-4
180
120
160
120
180
1.178
1.190
1.545
1.071
1.130
0.07853
0.07933
0.10299
0.07141
0.07533
B-5
Shim Rod
Fuel
C-1
C-2
0.803
0.922
C-3
C-4
C-5
Fuel
Fuel
Fuel
Fuel
Fuel
200
180
160
180
200
2600
0.05353
0.06147
0.06940
0.05747
0.04913
1.00000
0.862
0.737
15.000
It can be seen from closed analysis that the ratio of BUF-I to i is constant
for all core positions. This type of computation seemed adequate until after
much running time and many burnup calculations later, we achieved greater than
100% burnup on one of our shim rods. It was realized that while the LITR had
three shim rods, two were kept fully withdrawn and one was used to regulate the
power (this was the rod, which achieved >100% burnup). In order to correct for
this abnormality, it was decided after checking back that the rod was only 66%
in the core so the following correction was made,
DRNL-AEC - OFFICIAL
.
F
i
Determination of Burnup Factor II
The same method was used as in the determination of BUF-I with the exception
that only 66% of the burnup due the shim rod would be used. This not only lowered
the calculated amount of fuel consumed in the shim rod but raised slightly the
calculated amount consumed in all other core posicions since the total must remain
the same.
ORNIAEC - OFFICIAL
We will not make this correction to our hypothetical EBF core assuming that
the shim rod in B-2 is fully withdrawn during operation and the power is regulated
with the shim rod in B-4 (average position is 66% withdrawn).
Calculation of BUF-II
BUF-I
Core Position
A-1
A-2
A-3
0.05553
0.06347
0.07141
0.05947
0.05153
BUF-I
Corrected
0.05553
0.06347
0.07141
0.05947
0.05153
BUF-II
0.05691
0.06505
0.07319
0.06095
0.05281
A-4
A-5
B-1
B-2
B-3
B-4
B-5
0.07853
0.07933
0.10299
0.07141
0.07533
0.07853
0.07933
0.10299
0.04713
0.07533
0.08048
0.08130
0.10556
0.04831
0.07720
C-1
C-2
C-3
C-4
0.05353
0.06147
0.06940
0.05747
0.04913
1.00000
0.05353
0.06147.
0.06940
0.05747
0.,04913
0.97572
0.05486
0.06300
0.07113
0.05890
0.05035
1.00000
C-5
Determination of Burnup Factor III
Just prior to operation of the ORNL Research Reactor (ORR) the burnup:
. calculation was examined since the use of fuel during operation would be
much higher due to the higher operating power. Several problems were foreseen
involving cycling of fuel. For example, unlike the LITR, the xenon problem would
necessitate the changeout of almost entire cores during refueling. The removed
elements could be reused after xenon decay in assembling different cores. Since
the weight ascribed to a partially depleted fuel element depends on the burnup ...
calculation, the accuracy of the calculation as applied to individual elements
became increasingly important. It was felt that the burnup factor depended not
only upon the average thermal flux per element but also upon the quantity of
fuel per fuel element. Therefore, a burnup factor for any fuel element was now
determined by these two factors.
ORNL - AEC - OFFICIAL
According to this new thinking, the fraction of the total burnup whic
occurred in position i would be
OxNb - AEC - OFFICIAL
Burnup in i
Burnup in core
Be..
M
where
is determined from a flux map as before
is the ratio of fuel weight in i to fuel
c weight in the core
It was again recognized that the above conditions held only for a short time,
but was assumed to be reasonably accurate for a fuel cycle. The burnup factors
determined in this fashion again will not add up to exactly unity. This is
due to breaking up the product ratio into two ratios which are first determined
independently then multiplied together. Each burnup factor must be adjusted 80
that the sum will be unity by dividing each factor by the sum of the factors.
We can now lock again at our hypothetical EBF core and calculate BUF-III.
Calculation of BUF-III
235,
Core Position
(grams).
BUF-III
A-1
A-2
A-3
A-4
A-5
200
180
160
180
200
0.833
0.952
1.071
0.892
0.773
0.07692
0.06923
0.06154
0.06923
0.07692
0.06407
0.06591
0.06591
0.06175
0.05956
0.06624
0.06814
0.06814
0.06384
0.06159
B-1
1.178
B-2 (shim)
B-3
B-4 (shim)
B-5
180
120
160
120
180
1.545
1.071
1.130
0.06923
*0.03941
0.06154
*0.03941
0.06923
0.08155
0.04690
0.09508
0.04221
0.07823
0.08431
0.04850
0.09830
0.04365
0.08088
0.803
C-1
C-2
C-3
C-4
C-5
200
180
160
180
200
2600
1.041
0.862
0.737
1.000
-0.07692
0.06923
0.06154
0.06923
0.07692
0.06177
0.06383
0.06406
0.05 958
0.05669
0.96720
0.06386
0.06599
0.06623
0.06171
0.05862
1.00000
>RNL - AEC - OFFICIAL

1-AEC - OFFICIAL
ORNI -ALC - OFFICIAL
--------
-
-
---- -.-
ORNL-DWG 65-4424
U12) – 235U CONCENTRATION (g/linear in.)
W , WEIGHT 235U REMAINING (g)'
...
"T"
.
Figure I
5
10
15
L(inches from top of fuel section)
20
.

IL - AEC - OFFICIAL
ORNL-DWG 65-4123
UILISHIM - 235U CONCENTRATION (g/linear in.)
-80
W , WEIGHT 235U REMAINING (4)
0
0
Ziaure 21
10
15
L(inches from top of fuel section)
20.
.
OFFICIAL
ORNI - AEC - OFFICIAL

One other factor which must be made in conjunction with the above calculation.
If you will notice, the shim rods are corrected by the factor 0.854. This was an
experimentally determined correction factor to correct for the fuel in the shim
rod follower not being fully inserted into the core. This differs in that the
ORR shim rods are withdrawn as a gang to compensate for fuel consumption so the
correction was made on all shim rods containing fuel.
OINE - AEC OFFICIAL
Determination of Burnup Factor IV
The BUF-III calculation assumes that all the residual fuel in the element
is exposed to the average thermal neutron flux in the element. This, in reality,
is not true. Before proceeding to the determination of BUF-IV, we will briefly
examine the components of the burnup factor calculation, i.e., fuel distribution
and thermal flux distribution.
A. Fuel Distribution
During the course of depletion, the fuel is not burned evenly but acquires
a non-uniform distribution because more fuel is consumed near the longitudinal
center of the element than near the ends. This distribution has been determined
for the ORR * fuel elements by measuring the fission product distribution along
the element.
The following empirical relationships have been developed to describe the
actual fuel distribution along the element.
U(L),00 = 8.33 – (0.01164 + 0.0067594L - 0.000266071_) (200 – W)
U(L),40 = 10.00 – (0.01164 + 0.0067594L - 0.00026607L) (240 – W)
U(L) 41 in 5.88 - (0.03714 + 0.0037278L - 0.00020941?) (141 – W)
.
where
U(L)200, U(L),40, U(L) 147 refers to the concentration of fuel remaining
at L (grams/linear inch) in elements which originally contained 200-
grams, 240-grams, and shim rods which originally contained 141-grams
of fuel respectively.
L = the distance from the top of the fuel section (inches)
W = the calculated weight of fuel in a partially depleted fuel element or
shim rod (grams)
Figures 1 and 2 show the fuel distribution for various burnups for two types
of fuel sections under consideration.
B. Flux Distribution
Theoretical calculations have been used to establish the neutron- flux
distribution for unperturbed conditions and can at times estimate the perturbed
flux distribution. However, the core arrangements for the ORR does not resemble
a standard geometry and has. perturbing absorbers both in the core and reflector.
For this reason, the flux distribution can only be determined by flux mapping.
NE-AEC - OFFICIAL
A routine mapping of the ORR core is made about every six months or every!
time the core configuration is changed. These mappings are performed by inserting
cobalt wire monicors along the longitudinal centers of the fuel elements and shim
rods, raising the reactor to 30 kw for thirty minutes, shutting down, then removing
and counting the monitors.
ORNI - ACC - OFFICIAL
We do not feel that it is necessary to obtain absolute fluxes but rather
calculate flux ratios. The average neutron flux in the core , can be calculated
from the following relation:
- Reactor Power centres frontona/matt-sce
Reactor Power (watts) x fissions/watt-sec
Nu * Of(eff)
where
N = the number of 23%u atoms in the reactor
Of(eff) = the effective fission cross section for the 25u in the reactor.
For the ORR:
- 7036 x 1014
neutrons cm
Sen L
C
wt 235U(grams)
Figure 3 shows plotted against various core weights for the ORR. A typical
traverse along an ORR fuel element is shown in Figure 4. This was obtained by
cutting the cobalt wire into one-inch segment normalized to a peak of 1. The
traverse of an ORR shim rod fuel section is shown in
The neutron flux is very much depressed in the upper portion of the core
because of the poison sections of the shim rods. Although this distortion will
tend to become less pronounced as burnup proceeds during a fuel cycle and the
rods are withdrawn more, it will not completely disappear even if the fuel cycle
progresses until the shim rods are almost fully withdrawn because the fuel dis-
tribution is also distorted.
With this background information, we can now proceed with the calculation
of BUF-IV.
We will consider an element which originally contained 200 grams and has
been partially depleted to 180 grams. This element has been in a core position
which the = 1.000. If BUF-III were calculated from this data we would obtain
180
.
BUF-III
1 x ñ
but if we consider the components as described above we first look at the following
formulas.
U(L),00 = 8.33 - (0.01164 + 0.00675941 – 0.000266071) (200 – W)
and for W 4°480.
NL-AEC - OFFICIAL
ORNL-DWG 65-4147
01-01x po
-
4
.
6
:
235
Fegure 3
RNL - AEC - OFFICIAL
ORNI - AEC - OFFICIAL

ORNL-DWG 65-4116
IF(L) = 0.014 + 0.1010 L-0.002865 42 + 0.105 cos (0.3696 L + 0.564)
F(L) = FLUX NORMALIZED TO A PEAK OF 1.0
2
4
6
8 10 12 14 16
L(inches from top of fuel plate)
18
20
22
.
Figure &
NL - AEC - OFFICIAL
ORNL - AEC - OFFICIAL


*
*
S'*
u
ORNL-DWG 65-4115
F(L) = 1.090 -0.06167L + 0.000422_2 -0.093 cos (0.381L + 0.237)
F(2) = FLUX NORMALIZED TO A PEAK OF 4.0
2
4
6
8
18
20
22
10 12 14 16
L (inches from top of fuel plate)
Figure 5
ORNL - AEC - OFFICIAL
ORNI AEC - OFFICIAL

i
.
thead
.
2
bit
......
..
-
U(L),00 3.10 – 0.13519L + 0.00532142?
OxNb - AEC - OFFICIAL
P(L) - 0.014 + 0.1010L - 0.0028652? + 0.105 cos (0.3696L + 0.564) and
sal remo
f. 1.000
(L)
= 0.021 + 0.1507L - 0.004276L" + 0.157 cos (0.3696L + 0.564)
Therefore, in terms of calculating BUF-III for W = 180
24
ore
U(L) 200 al ?
BUF-III =
d,
200 ML
=
181.06
24M
However, if the intervals are made smaller, say l-inch, we have BUF-IV
mient
U(L200 ML
BUF-IV
=
200 41.1 x 177.51
1 j1
C
Dividing BUF-III by BUF-IV, we have 0.987. This means we are consuming only 98.7%
of that calculated by BUF-III.
ORNL - AEC - OFFICIAL
višinio =356=448

02:1
; ܢܝܫܝܙܝܺܪܽܬܝܺܚܪܽ
.
n
??
?
?
DURN UP CORRECTION FACTOR
.
DORITOS CORRECTION FACTOR FOR
THE TREE FUEL UNITS I USE
HITTE O.R.R.
::...
.....
...
.:
.
,
100 :120: : : 160: 100, 200, 220
RESIDUAL URANIUM (070.7.0)
.
Fegure to
ORNL - AEC - OFFICIAL
OPH1--OFFICIA!
Figure # shows the correction factor which must be applied to BUF-III to obtain'
BUF-IV for the various elements under discussion.
ORN - ALC - OFFICIAL
Again, we can examine the hypothetical EBF core.
Calculation of BUF-IV
235,
Correction
Factor
Core Position
(grams)
BUF-III
(BUF-III)xC.F.
BUF-IV
A-1
A-2
A-3
A-4
A-5
200
180
160
180
200
0.06624
0.06814
0.06814
0.06384
0.06159
1.000
0.987
0.972
· 0.987
1.000
0.06624
0.06725
0.06623
0.06301
0.06159
0.06621
0.06722
0.06620
0.06298
0.06156
180
120
B-1
B-2
B-3
B-4
B-5
160
0.08431
*0.05679
0.09830
*0.05111
0.08088
.0.987
0.970
0.972
0.970
0.987
0.08321
0.05509
0.09555
0.04958
0.07983
0.08317
0.05506
0.09550
0.04956
0.07979
120
180
C-3
C-1
200 0.06386 1.000
0.06386
C-2
180
0.06599 0.987
0.06513
150 0.06623 0.972
0.06438
C-4
180
0.06171 0.987
0.06091
C-5
200
0.05862 1.000
0.05862
1.00048
*not corrected by 0.854 as in previous BUF-III calculation
0.06383
0.06510
0.06435
0.06088
0.05859
1.00000
The following table illustrates the four burnup factors under discussion.
Comparison of Burnup Factors
Core Position
A-1
A-2
BUF-I
0.05553
0.06347
0.07141
0.05947
0.05133.
BUF-II
0.05691
0.06505
0.07319
0.06095
0.05281
BUF-III
0.06624
0.06814
0.06814
0.06384
0.06159
BUF-IV
0.06621
0.06722
0.06620
0.06298
0.06156
A-3
A-4
A-5
B-1
B-2
B-3
B-4
B-5
0.07853
0.07933
0.10299
0.07141
0.07533
0.08048
0.08130
.. 0.10556
0.04831
0.07720
0.08431
0.04850
0.09830
0.04365
0.08088
0.08317
0.05506
0.09550
0.04956
0.07979
C-1
C-2
C-3
C-4
C-5
0.05353
0.061147
0:06940
0.05747
0.04913
0.05486
0.06300:
0.07113
0.05890
0.05035
0.06386
0.06599
0.06623
0.06171
0.05862
0.06383
0.06510
0.06435
0.06088
0.05859
ORNL - AEC - OFFICIAL
10.
It is realized that the correction in going from UF-III to BUF-IV is
minor in the cases studied; however, the ORR is now being fueled with elements,
which originally contained 240-grams of 2350 and as depletion progresses the
correction factor to be applied becomes more significant.
ONNI - AEC - OFFICIAL
Comparison of Reactor spent Fuel with Reported Recovery Results
Listed below is a tabulation of spent enriched fuel as calculated by ORNL
contrasted with the recovery results reported by the recovery facility. Also
shown are the variances between our calculated weights and the reported recovery
weights. The experiences shown cover a period from May 1953 through January 11,
1966 - a period of slightly over twelve years.
From May 1953 through 1957 spent fuel elements resulted from the operation
of the Low Intensity Test Reactor only. In 1958 operation of the Oak Ridge
Research Reactor (ORR) was begun and the number of spent fuel elements requiring
recovery increasca substantially.
It is noted that of the 1,321 spent fuel elements for which recovery results
have been reported to date, the recovered material balance has been 99.988% of
ORNL's total uranium calculation and 100,15% of ORNL's 2350 calculation.
ORNL - AEC - OFFICIAL
Recovery Results on Enriched Spent Fuel Elements
(Weights in Grams
Number
of Spent
Elements
ORNL
Calculated Weights
-
Variances Between
ORNL Weights
and Reported
Recovery Weights
Reported
Recovery Results
235U
2350
235U
.
27
22
27
2,964
1,859
3,504
1,931
28
17
786
4
Period of Shipments
_ From_
_
То
: May 1953 December 1953
March 1954 August 1954
December 1954 June 1955
· June 1955 April 1956
April 1956 November 1956
June 1958 December 1959
January 1960 January 1962
January 1962 September 1963
September 1963 November 1964
November 1964 December 1965
December 1965 January 1966
Totals
7
479
151
410
3,237
2,134
3,806
2,262
1,619
18,034
44,630
46,937
38,158
29,831
3,161
193,809_
205
3,227 2,942
2,101 1,823
3,777 3,477
2,211 1,882
1,612 782
17,555 15,066
44,425 37,462
47,727. 40,072
38,158 29,387
29,831 25,082
-3,161 2,646
193, 785_160,621
29
308
321
: 228
195
- 21
1,321_
(790)
15,476
37,491
39,255
29,387
25,082
2,646
160,381
0
-24mm
(240)
ORNI - AEC - OFFICIAL
OXNL - AEC - OFFICIAL
".
..
-
i
.
.
.
ORNI - AEC - OFFICIAL
Fig. 1
Distribution of fuel along the length of a partially
depleted ORR fuel element
Fig.
2
Distribution of fuel along the length of a partially depleted
ORR shim rod fuel section
LR
Fig. 3
Average thermal neutron flux in the ORR core at 30 MW versus
weight of fuel in the core
Fig. 4
Flux distribution along the length of an ORR fuel element
normalized to a peak of 1.00
Fig.
5
Flux distribution along the length of an ORR shim rod fuel
section normalized to a peak of 1.00
Fig. 6
Burnup correction factor for the three fuel units in use at:
the ORR
ORNL - AEC - OFFICIAL
.
.!
.:..
S.
R
".
::

1.
1
1
T's
.
-
T '
!'!
Live?
KU
12.17
TILL
*
1
:
:
$."
END
.
.
.
-
Fit
1
S
.
.
.
.
DATE FILMED
12/ 29 / 66
.
BR
ZI 1
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i
ri
7,9
Ki
1"-",
-
.:
P