Archives
NYO 9717
MITNE-34
Is!..
C
MAY 22 1972
LISRARSS
f-)06
39
MODIFICATIONS
TO
FUEL CYCLE CODE "UEMUOVE"
by
Jo. A
Sovka and M. Benedict
Massachusetts institute of Technology
' Department of Nuclear Engineering
Contract No. AT(30-1)-2073
Apil
15,. 1963
TD 4500 CatLegory
UO-80 Reactor Thnlg
drt
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t e 'mtx T< C
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NYO-9717
MITNE-34
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.1
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UNCLASSIFIED
NYO-9717
MITNE-34
MODIFICATIONS TO FUEL CYCLE CODE "FUELMOVE"
by
J. A, Sovka and M. Benedict
ABSTRACT
Modifications have been made to the fuel cycle code
PUELMOVE to enable calculations to be made upon reflected reactors
without the use of the "reflector scvings" approximation.
The
modified code, called FUELMOVE II, is able to obtain thermal
flux distributions in both the fuel bearing regions and the
reflector, for batch and steady state bidirectionally fueled
reactors0
Also, reactivity control for batch fueling can now be
achieved by the use of a soluble poison in the reflector and
moderator in addition to the existent methods of fixed poison in
the core, control rods and burnable poison.
The natural uranium
fueled, heavy water moderated and pressurized heavy water cooled
CANDU reactor was used to test out the changes0
Comparisons of
results of fuel burnup and flux and power distributions with
previously obtained results show close agreement.
Included is a
description of the programming changes made to the code.
iaBLE OF CONTENT8
Page
Abstract
I*
II.
III.
IV.
Introduction . .
. . . . . . .
. .
. . .
Modification of Code ...............
A.
Continuous Seady State Fueling
B.
Batch and Discontinuous Outin Fueling
Results
. .
.
. .
. .
. .
.
.
. .
.
.
.
.
.
49
a
Is
4
. . . 10
.
.
.
. . . . . 16
. . .
A.
Continuous Steady State Bidirectional Fueling
. . . 17
B.
Batch Irradiation
. . . 19
. . . . . . . .
. .
. .
Appendix A.
Programming Changes for MOVE II
Appendix B.
Space and Storage Requirements
for
MOVE II
.
.
.
.
.
.
.
.
.
. . . 22
. .
. .
Conclusions
.
..
..
..
..
..
..
..
.
.
.
. . . 23
.
.
. . . 29
Appendix C.
Nomenclature
............
. . . 30
Appendix D.
"=O9I I Code Input Data Preparation
. . . 33
Appendix E.
References -.
.
.
.
.
.
.
.
. .
.
. . . 37
T
HODIFICATIO1,S_TOFIELCYCLE_CODE
FUEIJIOVE
I.
IRODUCTION
The purpose of this report is to describe improvements which
have been made in the fuel cycle computer code FUELMOVE,, previously
developed at MIT under this contract (1),
preliminary to undertaking
fuel-cycle analysis of the uranium-fueled spectral shift reactor
or core-and-blanket reactors.
There were two reasons why
FUELMOVE required modification before such reactors could be
treated.
One deficiency was that it contained no provision for
dealing with regions which did not contain a source or fission
neutrons, such as the reflector of the spectral shift reactor,
or a blanket.
A second was that the iterative procedure used
in FUELMOVE to solve for the flux distribution and criticality
condition became unstable and divergent when applied to a
reactor containing regions of substantially different compositions and nuclear properties.
Cases in which flux distributions
could not be evaluated by FUEIMOVE for this reason included a
core-and-blanket reactor, a reactor employing outin fueling with
high burnup, or a reflected reactor.
To deal approximately with reflected reactors, the "reactor
savings" boundary condition for the flux at the core-reflector
interface had been used in FUEI4OVE.
Thia is
often undesirable
because it does not give the correct flux distribution in the
outer regions of the core and it
does not deal adequately with
reactors whose reflector properties change with time, such as the
spectral shift reactor or a presaurised water reactor controlled
with soluble poison.
-
2 -
In reactors using outin tUeling with high burnup, Richardson (2)
found that the instability in the iterative procedure used to
solve for the neutron flux distribution could be eliminated by
replacing the Crout matrix reduction procedure used in FUELMOVE
by a method of successive displacements,
the so-called extrapolated
Liebmann method (3).
The two principal changes in FUELtOVE made in the work
described in this report are:
(a)
extensioa of the code to regions which do not contain
a source of fission neutrona,
such as a reflector or
blanket, and
(b)
use of the extrapolated Liebmann method to solve for
the flux distribution, which is here shown to be
applicable to reflected reactors as well as to the case
treated by Richardson.
As a test case for the modified code, the CANDU reactor
previously studied (1)
with F1ELMOVE was chosen.
This is a
pressurized water reactor, cooled and moderated by D20, fueled
with natural uranium and provided with a thick radial heavy
water reflector.
Section II of this report describes the modifications made
in FUEIMOVE to permit it
to handle regions which do not contain
sources of fission neutrons.
Section III sumarizes the results
of fuel cycle analysis of the CANDU reactor using the modified
code and compares these results with those obtained previously
with the original code (1)
and those given by the Atomic Energy
of Canada Limited (4) for this reactor.
The Appendix describes
- 3 the programming changes made to FUELMOVE and outlines the additional computer input data needed for the modified code.
L
-
II , MODIFICATION OF CODE
Of the two parts of the FUELMOVE code,
only the latter
required change.
"FUEL" and "MOVE",
For brevity,
in this report,
the modified code will be referred to as MOVE II,
original code as MOVE I.
and the
The full name for the modified code
is FUELMOVE II.
The description of changes made in FUEIMOVE are divided
into two parts.
The first part deals only with those changes
required to allow calculations for a reflector region in a
reactor using continuous steady-state fueling, which, for the
CANDU reactor, is steady-state bidirectional fueling.
In
steady-state fueling, control poison is not present in the
reactor.
The second part describes changes made to permit
treatment of methods of fueling in which soluble poison is
present
in the moderator and reflector, such as batch or discontinuous
outin fueling.
A.
Continuous Steady-State Fueling
1.
Slowing Down Density, q, and Fast Non-Iakage
Probability, P
The fast non-leakage probability, Pl, was defined in
NYO 9715, Equation (4C11),
and calculated in MOVE I as
2
PA,
-,I
Since in the reflector, both) YZ
___
and
(1)
are zero, the denominator
becomes zero and P1 becomes infinite by this definitiono
Likewise, the slowing down density, q, is defined by Equation
(4012) as
Here again,
(2)
4z 1 $02
q
Xf, is zero in the reflector, and thus by this
definition "q" becomes zero.
Therefore, according to the reactor
physics model chosen, the slowing down density, q, and the fast
non-leakage probability, P1, are undefined in the reflector region.
2.
P
C
Criticality Factor
and q were required in MOVE I to calculate the reactor
criticality factor, C, as given in Equation (3)
which is
the
same as Equation (4035) of NYO 9715,
IRL JZL
S((qPpV)
C = 'IRL JZL
ZZ
[(7,,2 - D2 2 2)v],
ial j-1
This is simply a flux-volume-weighted neutron balance for the
whole reactor where C is defined as the ratio of the total thermal
neutrons produced to the total thermal neutrons abosrbed and
leaking out of the core .
However, the product (qPp) is defined
only for the fissile fuel bearing region because for the
reflector region, q is
zero and P
product is indeterminate.
is
infinite and therefore the
Nonetheless, there must physically be
production of thermal neutrons in the reflector, due to
thermalization of the fast neutrons that leak out of the coreo
This inconsistency can be avoided by not performing the
intermediate step of calculating q and P1 but rather considering
the thermal neutron balance equation as given by Equation (409)
and (4) below
.MD
-D2
92
7
2
(Z + 3Y)2
-rl
+ EV,f2 -D2
.1(Z
P__
(12p)
A 2
P
(4)
The left side of (4) gives the loss of thermal neutrons by leakage
and absorption while the right side gives the production of
The factor in the curly braces contains the
thermal neutrons.
production of fission neutrons including the fast effect minus the
fast leakage.
It
is
multiplied by the resonance escape probability
and divided by a term that takes into account the resonance fission.
The local criticality factorCi,, is then the thermal
production over the absorption, i.e. the right side over the left
side.
To obtain the core average value, the local values are
flux-volume-weighted as given by Equxation (5)
IRL JZL
tV.
D2Y2O 2
+ '%W) - -2
(
V
IRL JZL
1-1 j =l
-. 219'2 +
+ ("0V+
+3 Xw
2
12
VJ~
ji,
(5)
(Note that X
in the denominator would be zero for the unpoi.soned
criticality factor, but would have a value for the poisoned core
criticality factor.)
The local value of C at the mesh point
(ij) can now be evaluated for either a fissile region or for a
non-fissile region such as the reflector.
zero, C
in
the reflector becomes
Since ) X
and
are
2
D2O2
pr
2
92
V
CreV
D2V
-+
a2)0
id(6)
'
(Z + 2
#
Equation (6) can also be derived by a consideration of the neutron
balance equations in the reflector in the following manner;
The equation for the fast flux in the reflector is
o
- Z
D
(7)
Here the first term is the positive contribution to the flux at a
point due to leakage ard tke second term is
fast flux by slowing down.
D2 2
Here the first
term is
The thermal flux equation is
(-
2
the removal of the
+
w)02 + Pz 1 s
(8)
=0
the leakage term, the second is
the loss
due to absorption, while the third is the production of thermal
neutrons.
This last term is simply the fast flux removal term
times the resonance escape probability which, although it
usually be 1.0 in the reflector, it
is
will
retained for generality.
Solving for the fast flux OL from Equation (8)
D
2
+ (z + x )2
From (7)
Therefore,
~l~l
j 1V2
[
0%~~32~(
+ 2:w)021
(10)
.p
Now substituting (10) into (8) gives the thermal balance equation
as
D2 V00-
or, if X is
(z + Z,)0a + PD F2
D2 V
+(Z-+X0
2
0
2
(11)
independent of position,
(12
)
and (11) becomes
-a
D2 Vgf9
2
(z +
zV)#2
+ pV#
2
D 2V
2
+4 (0+z
+
p
(Z
+
)
£0)#
(13)
The first two terms of (13) give the loss of thermal neutrons
due to leakage and absorption, while the third term gives the
production.
The local flux-volume-weighted value of the
criticality factor, C,
in the reflector is thus
f2
2
(14);
Cref
F2
Ed Jg
*V
which is identical to Equation (6) above.
Therefore, it is not necessary to calculate q and Pl as an
intermediate step towards calculating the thermal neutron
production term and, in addition, this would not be possible for
the reflector region.
However, by using Equation (5),
as is done
in MOVE II, the thermal neutron production term in the reflector
creates no difficulty.
It
should be pointed out that the two seemingly different
expressions for C, Equations (3) and (5),
are in fact identicalo
If one substitutes the value for Ps, given by Equation (1), and
q, given by Equation (2), both as defined in NYO 9715, then the
product (pqPOv) is equal to the numrator of Equation (5).
3o
Total Fission Cross Section, Xi
The only other place that q and P
and Central Flux, #0 .
were required in MOVE I
was in the calculation of the total fission cross section, E
given by Equation (4033)
xTOTf'i)
f(i1,j)
-The value of I
9
,
as
+x
1,
P1
(
D~
L7-]
(15)
(5
was then used to calculate the absolute value
of the central flux according to Equation (16)
given by (4034)
IRL JZL
V
PDENAV
-
IRL JZL
.6,1'~~
3*.14 x 10-11
=1
(TOT
(16)
V
1=1 j=1.i,
However, for a reflected reactor, the average power density,
PDENAV, is obtained only for the fuel-bearing region so that the
summation in (16)
over the core.
would not be over the whole reactor,but only
has a defined value for the core region,
STOT
f
but not for the reflector because PIis infinite.
Therefore,
by limiting the evaluation of
TOT and the summation of (16)
to the core region only, the correct value of
is
4
obtained.
B. Batch and Discontinuous Outin Fuelin
The batch and discontinuous outin fueling methods require
the use of a neutron absorber to control the excess reactivit;'
of the reactor after new fuel has been added.
This can be done
with control rods, poison in the fuel, or soluble poison in the
moderator.
In NYO 9715 and thus in MOVE I, no distinction needed
to be made as to how this poison was applied, although it
was
possible to specify zonal removal of an absorber (such as
control rods) or to use a burnable poison.
The amount of poison
needed to keep a reactor critical was determined in the form of
a normalizing factor, X
, which was obtained from a flux-volume-
weighted neutron balance by Equation (4031)
P p - Z+
D2?2
I
2
(17)
~wl
where £wn
relative amount of poison, which usually is
1.0.
Since the use of a soluble poison in the moderator and
reflector is a possible (and usually preferred) method of
controlling reactivity, the relative factors £wn will no longer
be constant over both the core and the reflector.
The common
basis must now be the concentration of poison in the moderator
and reflector which will in tnrn contribute different amounts to
the total thermal absorption cross section in the two regions
because of the difference in the volume fraction of moderator
between the two regions.
In addition, the higher average flux
-1
11' 1
in the moderator relative to that in the fuel must be taken
into account.
In MOVE I, an initial estimate for the normalizing factor
X.1was made by using Equation (17).
were obtained by adjusting I.
was equal to 1.
Subsequent refined values
until the criticality factor C
In MOVE II, the adjustments are made to a
concentration factor, which in turn affects the local macroscopic absorption cross section and thus C.
Macroscopic Absorption Cross Section
1.
The following describes how the absorption cross sections
are calculated in MOVE II to account for the different relative
effectiveness of the soluble poison in the moderator and in the
reflector.
(a) Reflector.
The macroscopic
absorption cross section of
the poisoned reflector is given by (18)
-
N FR + N04
(18)
where NRa = absorption cross section of the unpoisoned reflector,
Ngo
= absorption cross section of the poison.
Expressing the number of poison atoms per unit volume in
terms of a concentration such as parts per million, PPM, results
in (19)
No
PR
(19)
PPM
A x 10
where.
No = Avogado'Is number = 6,025 X 10
p
= density of reflector (liquid)
amoe
-
12 -
A = atomic weight of poison
PM = grams of poi8on per 306 grams reflector liquid.
(b)
Core region.
For the core region, account must be taken
of the fact that the thermal flux in the moderator region of a
lattice cell is greater than in the fuel region and that.the
volume of the moderator occupied only a fraction of the total
Therefore,
cell volume.
in obtaining an average cross section
for flux calculations, the absorption cross section for the
moderator must be multiplied by the moderator thermal disadvantage
factor.
Let the average thermal absorption cross section in the core
be defined as in (20)
core
where 7
2
(20)
7i;
average thermal flux in region 1.,
= thermal absorption cross section in region i,
V, = yolume of region i.
Rewriting (20)
in the slightly different form given by (21)
Zfmm
V+
ev
core
where
(21)
m refers to the moderator region,
j refers to all regions other than the moderator, and
(m + j)
.
Differentiating Equation (21) with respect to Xam and assuming
that the flux shape through a lattice cell remains constant with
- 13 varying moderator cross sections (which is
the same assumption
as made in NYO 9715)
core
mm
Therefore
M m(23)
obtains
Dividing (23) through by?
core
core ="fMf"M
(2)
c.0iiore
core
or replacing differential quantities by finite differences
core.
rrmm
(25)
ciiore
ore
Now the core absorption cross section with poison in the
moderator will by given by (26)
a
/
core
a
core
1 +
1
core
(26)
core
where the primed value includes moderator poison.
From Equation
(25) this becomes
or
core
oe
acore
Score +
++
PO+V' 1
m 0 TDFMOD
(27)
(28)
~ 4
where TDNOfD = thermal disadvantage factor for moderator
ofV
(29)
i i
This last quantity must be calculated separately and read in as
part of the input data.
The change in moderator absorption cross section, 6Z;is the
poisoned cross section minus the unpoisoned cross section
La
za
La
NR0,
=NeR, + NA
(30)
N,
Equation (30) and the subsequent derivation assumes that the
reflector material is the same as the moderator in the core region,
Thus, from 3quations (20), (25),
as is usually the case.
core
N0 sR PP,
A x 10P
ra-
TDPNOD
and (29)
(31)
Defining
o
P
(32)
core + FACMOD * TDFMOD * PPM
(13)
FACMOD =
10 A
gives for the core region
core
and likewise for the reflector region
(34)
+ =FAMOD - PPM
Therefore, an initial estimate of the poison concentration in the
moderator fluid in MOVE II can be made by a flux-volume-weighted
neutron balance as given in Equation (35)
similar to that shown
by Equation (17) for NMVE I
)i
PPM
++
j=1
I
rFACMOD
1FACOD
211
- TDFPoijVi
imi
D2V?2
+
I
1iICORE+l
(35)
where the summation in the denominator is divided into two parts-one including only the core region, and the other including only
the reflector region
S16
The CANDU remator was used to try out the successive modifications which were made in FDEIMOVE so that comparison could
be made with previous results (1).
No cost analyses were
made in the work reported here, however, as this portion of the
code was not changed.
Physical properties of heavy water used for the reflector
of this reactor are listed in Table 1.
Table 1
Properties of D 2
in CANDU Reflector
Density
1.0986 g/cm 3
Thernal absorption cross section, M.
0.6594 x 10'cm-
Resonance exeape probability, p
1.00
Diffusion coefficient, D
1.002 cm
Fermi age,
143.5 cm2
'
The inner and outer radii of the reflector are:
Inner
230.2 cm
Outer
299.7 cm
Part A of this section describes the tests that were made
of successive changes in FUELMOVE that were required to deal with
reflected reactors using steady-state, continuous, bidirectional
fueling, in which control poison is not present in the reactor.
Part B describes tests made of the further changes that were
required to deal with the batch fueling method, in which control
poison is present.
Tabie 2 eoMaies reultts obtained from the successive changes
made in FUELMOVE with those obtained from Move I and reported in
NYO-9T5 (1) for steady-state, continuous, bidirectional fueling
with natural uranium.
Table 2
Steady-_tate ContinuousBidiretior!l Fueling
Natural Uranium
CANDU Reactor
AIL M0
MWe
WD/1
Iurnup,
Procedure
Reflector
for
Plux
Solution Criticality Savings Central
Averag
Zone
Used
Procedure Factor, C
Code
max. to
Average F1ll
Peak
Power Power
Power
Density Density Time,
Ratio Years
kw/1
Old
Yes
11,620
9,080
17.56
2.040 1.33
2. MOVE I. Liebmann
Old
Yes
11,650
9,087
17.464
2.015
1.33
3. MOVE II Liebman
New
Yes
11,650
9,087
17.464
2.015
1.33
4. MOVE II Liebmann
New
No
11,830
9,219
17.338
1.999
1.349
No
11,320
8,850
17.01
1,979
1. MOVE 1
5. AEWL
Crout
The first row summarizes results given in Report NYO 9T15,
Table 6.4, which were obtained with MOVE I, using the reflector
savings approximation end the Crout reduction procedure to solve
for the flux distribution. Rows 2, 3 and 4 give results in which
changes were made sue8essively in the computation procedure.
In
row 2 the extrapolated Liebmann method was substituted for the
Crout reduction method, with negligible changes in results.
row 3 the revised procedure for evaluating C described in
Section II was used in addition to the extrapolated Liebmann
In
I
method, again i,th
18
negligible change in
results.
The agreement
between rowl 1, 2 and 3 merely confirma the accuracy of the revised
calculation procedure, as the same reactor model is used in all
three cases.
In row 4 the reactor model is changed, by solving for the
flux distribution in the reflector as well as in the core, instead
of using the reflector savings approximation to represent the
effect of the reflector on the flux distribution in the core,
as was done in rows 1, 2 and 3.
Row 4 uses the fully modified
MOVE II code, with the new procedure for evaluating C and the
extrapolated Liebmann method for solving for the flux distribution.
The improved representation of the reflector in row 4 increases
burnup by about 2% and decreases peak power density by a small
amount .
The last row gives results for the same reactor and fueling
method obtained by AECL (9) using a different two-group fuel-cycle
code.
The Canadian results predict a burnup lower by about 4%
and a peak power density lower by 2% than MOVE II.
Comparisons of the relative thermal neutron flux in the
radial direction are shown in Figure 1.
The three cases using
reflector savings give almost identical results and are not
shown separately in the figure.
MOVE II,
for the reflected
reactor, obtained a flux which agreed well in the central core
region, but was slightly higher than the MOVE I flux in
core region.
In the reflector region, MOVE I
the outer
predicts a thermal
flux substantially greater than that obtained by the AECL twogroup method.
;.,
~~7: 7
it
IT
I
IAr~
24J
.#
ALr
4
41
KbI
14
1-rL-
I :
-T
_;J,14
I 7I
7~
.1
k
'4
-a
1
i
, ,
4
i
I
rIiI
,I ' -
,
I
;I
I'
-'
It
is
felt
that the higher estimates i
reflector thermal flux obtained Crop.MOVE I
fuel burnup and
in comparison with
AECL are probably due to the rather coarse mesh spacing used in
the region of the core reflector botudary.
Both NOVE I and
MOVE II can handle only 10 mesh points in the radial direction
which limits the number of points in the reflector region to
3 to 5, leaving 7 to 5 for the core.
In the cases tried, 3 mesh
points were specified in the reflector.
Therefore, it is
probable that closer agreement would be obtained by increasing
the number of mesh points., This, however, will increase computer
time ever further which may not be justified for a survey code
such as this.
Even now, introducing the reflector region into
the calculations has multiplied the computation time for the
code, not including cost calculations, by a factor of 3. Both
MOVE I and II, using the reflector savings, obtained a converged
solution in 0.4 to 0.5 minutes on the 1BM 7090 whereas MOVE 1
for the case with the reflector took 1.4 minutes.
B.
Btch Irradiation
A comparison of results obtained from successive changes to
FUELMOVE are shown in Table 3 for the batch irradiation of the
natural uranium fueled CANDU reactor,
In lines 1 and 2, the
"reflector savings " approximation was used and a uniform poison
cross section was added to the core to maintain criticality*
Line 3 gives the results for the reflected reactor using soluble
poison (cadmiumv) in the moderator and reflector to reduce reactivity.
In all three oases, the results agree very closely.
- 20 -
Table 3
Batch Irradiation of Natural Uranium Fueled
CANDU Reactor at 200 MWe
Procedure
for
Flux
Solution
Procedure
Code
Reflector
Fuel Burnup, MWD/
Savings
Used
C
1%
Central
Average
1. MOVE I
Crout
Old
Yes
68og
3760
2. MOVE II
Liebmann
New
Yes
6847
3713
3. MOVE II
Liebmann
New
No
6955
3730
-.
~.-
I -
Data used for the soluble poison case are shown in Table 4.
STable 4
a
for the Control Poisonf
of.L Nia
lUaI=u_
Soluble Poison
.
.
.
.
.
tjich
uled,_CADU Reactor
.
Atomic Weight of Poison . .
.
.
.
Cadmium
112.41
.
Microscopic Absorption Cross Section,
Moderator Density . .
.
.
Irradgtion
.
.
. .
. .
Moderator Thermal Disadvantage Pactor
(from Ref. (1)) .
.. . . . . . . .
3001.5 barns
1.09859 s/ce
1.8232
This is the Westcott "average" cross section defined as in Ref. 4.
99 - - y - -
r-ay1 0,(
s
for a moderator neutron temperature of 530 C (Ref. 5).
(*
g
VS
for Cadmium
2460 barns (Re.f
-
4)
1.431
(Ref, 4)
0.035
(Ref. 5)
.740
(Ref.
5)
Figures 2 and 3 show the radial thermal flux distribution
for CANDU at the beginning and end of batch irradiation respectively,
from MOVE II results for both reflector savings and reflected
cases,
Results from MOVE I are not shown as they were almost
identical with the MOVE II "reflector savings" case.
It is seen that the flux distributions are in close
agreement.
The flux peak in the reflector at the beginning of
batch irradiation is not large because of the presence of
poison in the reflector, which results in a rather high maximumto average power density ration as shown in Figure 4.
However,
the reflected end-of batch distribution shows a substantial peak
just inside the reflector region.
is now relatively flat.
The power density distribution
This is due partly to the fact that the
fuel burnup at the center is higher than elsewhere, and partly to
the presence of a highly effective reflector of now unpoisoned,
pure D2 0, which increases the flux at the core-reflector boundary.
It is interesting to note that the flux in the reflector at the
end of batch irradiation is higher than at any point in the core.
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-22IV. CONCLUSIONS
Changes have been made to the fuel cycle code FUELOV
making it possible to treat the reflector region without the
use of the "reflector savings" approximation.
Flux distributions
can now be obtained in both the core and the reflector.
Fuel burnup., power densilty and other results agree well with
previous NOVE I results and with those from more refined two.
group methods.
For the present, progra=mLog chanSes have been made only
to subroutines treating the steady-state bidirectionally fueling
and batch irradiation methods.
Investigations are continuing to
include the treatment of the discontinuous outin fueling method.
-I
APPEtix. A
Pgraming chanesa
for NOVE Il
The MOVE II code can be used both for problems utilizing the
reflector savings approximation and problems that specify a reflector region.
The following is a description of the pro
changes that were made to MOVE I which resulted in present
solution by MOVE II.
Modifications were made mostly to the
(MAIN) program and subroutines SPACE2, SPFUN and SPPUN2.
Minor
changes to other subroutines are indicated below.
MAIN) MOVEPR
It was necessary to change the MAIN program to allow the
input of a parameter specifying the outer radial edge of the
core.
This is done by reading in an integer called ICORE which
is the radial mesh point equivalent to the outer boundary of the
core.
This numberb ICORE must be specified whether the problem
uses the reflector savings approximation or whether a reflector
region is
included.
ICORE must be not greater than 10 for problems
using reflector savings, and will thus be equal to IRL, the total
number of radial mesh points.
For problems which include a
reflector region, ICORE should preferably be not more than 7
ard not less than 5, leaving at least 3 mesh points for the
reflector. Since ICORE is used in several of the subroutines,
it
is now included in the common storage of the MAIN program and also
in the subroutines SPACON, PTPRCP, NCGTH7, SPACE2, SPACFX, SPFUN,
SPFUN2, BITDRCT, COST and SHUFFL.
In problems treating the batch irradiation of fuel, poison
is used to control the excess reactivity.
The estimates for the
poison required are made in SPFUN, 'The first estimate of poison
Dl?.
requires'a value for the fast leakage, --
However, since
the fast leakage is calculated in SPFUN 2, which comes after SPFUN
in the program logic, MOVE II Approximates the fast leakage as
being equal to the thermal leakage, -D 2B 2 which is specified in
the input.
This equivalence is made in MAIN at the beginning of
In all subsequent iterations and
the batch irradiation section.
-estimates of poison, the fast leakage from the previous converged iteration from SPFUN 2 is
transferred via COMMON to SPFUN.
SPACE OA
The purpose of SPACE 2 is to connect and control the subroutines which calculate the spatial flux and power distribution,
the criticality, the control poison and other reactor properties.
It requires at each mesh point, the 7 properties obtained in
Z
-
PTPROP (i.e. Z,
), Z,,
(
)
p) and p),
'(1
the spatial constants from SPACON, IRL, JZL, PDENAV, and initial
estimates of -D2 e,
P 1 and the flux shape.
In MOVE II,
a control
parameter called ISOL is now read in by SPACE 2, specifying whether
soluble poison in the moderator and reflector to be used in
controlling excess reactivity.
soluble poison is
If
ISOL is
greater than zero and
to be used, then additional data must be
specified giving the atomic weight (ATPOIS) and microscopic
absorption cross section (SIGPOIS) of the poison, the moderator-
reflector density (RHOMOD) and the moderator thermal disadvantage
factor (TDFMOD).
These are also read in at this point.
If ISOL
is zero, fixed poison as in MOVE I will be calculated and the
above data is not required.
SPACE 2 in turn calls subprograms SPFUN, SPACFX and SPFUN2.
The purpose of SPFUN is
to calculate the elements of the
coefficient matrices "d" and "e of equation (4015) of NYO 9715
for use by SPACFX which in turn calculates the spatial distribution
of the thermal flux.
It
also calculates the amount of control
poison required to keep reactor critical.
In MOVE I,
the poison
management was made by the addition or removal of an additional
macroscopic absorption cross section over the core.
MOVE II
can
treat reflector-savings systems as MOVE I and also reflected
reactors with either fixed poison in the core or reflector or
soluble poison in the moderator and reflector.-The estimates of
control poison are made by the use of equation (35) given in
the above text, where the factors FACKOD and TDFMOD are set
equal to 1.0 for fixed poison calculations (ISOLaO) or computed
from input data for soluble poison calculations (ISOLl).
SPACFX
SPACFX calculates the thermal neutron flux distribution for
the reactor using the coefficient matrices "d" and "e" obtained in
SPFUN.
As is
described in NYO 9715, the fast flux is
eliminated
from the two group diffusion equations giving one partial
differential equation for the thermal flux given by Equation (4),
p.
5 above.
This equation is
written in five point difference
form and the resulting difference equation is
then satisfied at
every mesh point in the reactor by an iterative technique.
MOVE I
used the modified Crout mtrix reduction iteration method which
was found to be unstable for the outir fuel management scheme
for enriched fuel.
Richardson (Ref. 2), however, found that the
extrapolated Liebmann iterative method gave satisfactory results.
The technique is described in detail in Ref.
(3),
(6),
(7) and (8)
C 26 ,
and only a brief
uimmary is given here.
Rearranging Equation (4015)
of NYO 9715 in the following form:
d
d
dd
±4i
d
1
4
ii,
d
e1
P3,1~
where the subscripts ii J pertain to a particular mesh point.
The overrelaxation parameter F
'is then inserted to give, for
( + 1) iteration
the
, y izp2+1
+1 __
e~ 3 a. d 1 3
,j
+ F
1
+
e
-~h
ed -d+1,
+ F -
-1,
1
- d
3
i,
di.a+5
-
The factor F must be less than 2 and more than 1. A value of
1-5 was used in the cases studied.
The initial flux shape is estimated in the MAIN program while,
subsequently, when the SPACFX subroutine is left and reertered,
the flux shape from the previous converged calculation is used
as the initial estimate.
The extrapolated Liebmann has several other advantages
over the modified Crout reduction method in this application:
1.
Much less computer storage is required
2.
Only one FORTRAN statement is needed for the iteration
whereas about 30 were used for the Grout reduction method.;
Both iteration methods used approximately the same amount
S#27
-
of time.
The present edition of SPACIX contains the mesh point
specifying the core-reflector boundary, ICORE in the CONNON
statement.
SPFUN 2
SPFUN 2 calculates at each mesh point and also the core
averages of: the criticality factor:'( :; the fast non-leakage
probability, Pl; the thermal neutron production term
(IF"+ X),
the thermal leakage term (-Di)
D2
2
and the power densities.
In
addition, the reactor criticality factor with control poison,
CW; the flux magnitudes,
1rz; and the maximum to average
power density ratio are obtained.
The changes as outlined in the main text were made:
(a) Calculating slowing down density, q, and fast nonleakage
probability, Pl, only to the core-reflector boundary and
setting the values in the reflector equal to zero.
(b)
Modified formula for calculating the criticality factor, C,
both with and without poison.
(c) Changed limit of sumation in radial direction from
IRL to ICORE for calculating the average power dentisy
which is used to set the absolute value of the thermal flux.
BIDRCT
This subprogram evaluates the flux time and the seven fluxtime properties at each mesh point and calculates the properties
of the discharsed fuel for the cost analysis for the steady
state bidirectional fue1 M.ovement.
In evaluating the average properties at each mesh point for
the two different fuel exposuren at that position, the resonance
capture terms are weighted with the slowing down density while
thermal properties are averaged with the thermal flux.
Since
this averaging procedure iz not necessary for the reflector
region, it is made only for the fuel bearing region, I.e. from the
center to mesh point ICORE.
APPENDIX B
Spce and StoragefRequirements for. MOVE II
Space requirements by the above subprograms have remained
essentially the same as in MOVE 1.
The amount of COMMON storage
has been increased to include the core boundary (ICORE)
the
fast leakage (C40), and the soluble poison parameters.
Now the
largest amount of COMMON storage required is 6858 locations
for subroutine SPFUN2.,
AP1,6l1'IDEIX
C
Nomenelature
1. English Letters
A
Atomic weight of soluble poison
C
Criticality factor defined in Equation (12)
Di
Fast neutron diffusion coefficient
D2
F
Thermal neutron diffusion coefficient
Over relaxation parameter in extrapolated Liebman
iterative method
FACMOD
Moderator factor defined by Equation (32), p. 1,2
g
Westcott cross section parameter (Ref. 4)
N
Avogardo's number
.
N
5413
Nuclide concentrations of U235, U236, Fission Products,
U238, Pu239, Pu240, Pu242, and Burnable poison.
N
Number of atoms of poison per unit volume of moderator.
NR
Number of atoms of reflector medium per unit volume
p
Resonance escape probability
PDENAV
Average power density
PP14
Parts per million of soluble poison in Moderator
q
Slowing down density
r
Westcott cross section epithermal index (Ref. 4)
s
Westcott cross section parameter (Ref. 4)
TDFMOD
Moderator thermal disadvantage factor
V
Volume of region
p
2. Greek
tjer.
6
Fast fission factor
a
Ratio of capture to fission crosis section
q 31 Ratio of capture to fission cross seftion of U238
a
liasion neutrOns per thermal aasorption
Fision neutrona per resonance absorption in U238
Mioroecopia absorption
neutrons
arots secion for 200 n/se
Effective Westcott croas adotion
Averae WestCott cross.section
£ Masoopt
absorption cross section
rdmoval cross section for tast neutrons
MaOrosopte
f1
MaroscopIc fission Cr455 sectich
Total macrosoapio fission cora
Equation (15)
Z
section defined by
Naaroscopic absorption cross sedbinof
Mod poison
Fast nqutron flux
Thermal neutron flux
Moderator density
3. !o'rtran Frospra
VtboaL1
ALAQ
Denominator of
4aragan coeffiolent
ATPOL
Atomic weight of poisn
D
Ditfuslon soetticient
past tinion factor
FACE D
OM
TI
d4en4t
Vtsa
r factor defined by Beitieu
(32)
oInt specifyiIng cter radial edge of core
s1ge poison control par
taMetr
AT
kuibeer of arangian fit points for f. tintS fit Or
monize4 properties and nuclide ooenentratione
7W
FlNT2E
ttisittmg
power density
-
RHOMOD
32
-
Moderator density
SIGPOIS Microseopic absorption cross section of poison
SIGMSM
Samarium croas section
Moderator thermal disadvantage factor
VL
Volume of fuel in lattice cell
'fETA Flux time step
-
33-
tPPENDflL D
:ave I,.CodeInpta
D1.
temration
The HOVE II code can be used to make fuel oycle analysts of
reactors either using the "reflegtor savings" approximation or
including a reflector region.
At present, only those subroutines
of the pzogram that treat bidirectiOnal fuelling and batch
fuelling methods haY? been modified to allow treatment of a refleotor region.
The discontinuous outin fielling scheme is
similarly being modified but has not yet been completed.
The input data preparation for MOVE II is identical to that
required by MOVE I as described in NYO 9715, with only thE
following additional data required:
(1) ICORE (Format 13, card 7, colasn
46-48)
e.g. 7, in cases studied
(2) Reflector reactor physics parameters in the same
format as the FUEL code output for the core region.
This is described in more detail in Appendix D2.
(3)
For batch Irradiation cases using soluble poison,
ISOL = I (Format 13, on the same card as POOH,
columna 13-15, right after COST inpat data).
For control by addition of a constant absorptimo
cros
section, this can be left blana
(4) if ISOL = 1, the neat card must spectfy paramete
the solable poison control, i.e,
ATFOIS, SZQPO$B,
RNOMD, TDKOD (Format 6712.6).
e.g., see ?able 4.
if I3&L
s
Q, this card must be left out.
for
D2.
Reflector Ream=f Phsica Ptcnprties
In order to make calculations for a reflected reactor,
physics parameters must be specified for the..reflector.
The
format of this data is the same as that supplied for the core
region by the F!EL part of the code.
It is therefore necessary
to prepare separately and arrange the reflector properties in the
manner shown in Table Ai3 of WfO 9715, and Table 5 below.
- 35 M
ci
bv
- MOVE--
COlUMn
Ca r-d
Number
Type
1-12
I
JAY
13-24
F
ZETA
25-36-
F
EPSI
37-48
F
49..60
F
05P
61-A72
F
TAU
143.5
(3)
2
1--12
F
D
1.002
(3)
2
13-24
F
PDLIM
0
2,
25-36
F
SIGNSM
0
1
2
NOTE:
Symbol
7
3.000E-04
(1)
(1)
0
0
9. 2484E-12 (2)
The following g roup of 3 cards ia
eachl
ExPAple
repeated JAY times but
contains ±dentical numbers except for Q/ZERTZ, the
flux time step.
1
1
1-12
F
13-24
F
Q/ZETA
e',
25.36
37-48
49-60
61-72
2
1-12
2
13-24
2-
25-36
37-48
F-
49-60
61-72
ma
(1)
0
0.6594E-04 (4)
F
Zf
0
0
:0
F
0
SF
1.000
F
(1)
F
F
N5
N5
O
0.
N67
'0.
36 -
Item
Colum
Card
NAmber
Type
1-12
NS
0.
13-24F
N9
0.
0'
3
25-36
F
Nib
S7-48
F
N0.
.3
49-60
3
61--2
F
N1 2
0.
N13
*
NOTES1
(1) These should be the same as the corresponding values for
thlue fuel-bearing regiona properties as obtained by FUE.
(2)
C5P must be the same as used in the core region because
only one COMHON
(3)
location is
The values of?
reserved for it.
and, D used In this study are the same
as those for the core although the values for pure rgflector
would be more correct.
(k')
pare D20-
The macroscopie abso-rption cross section for 99.8%
APPENDIX E
Reference&
(1)
NcLeod, N. Bi, N. Benedict, eti &I., "The Effects of Fuel
and- Poison Management on Nuclear Power Systems, " NYO 9715.
(2)
Richardsoni N-, C, "The Effectb of Cha
Conditions on Energy Costs in Zirealoy
rig Economic
Clad, Pressurised
Water Reaetors, " MITNZ-27, December 1, 1962.
(3) Hansen, N. F., "An irnential Extrapolation Method tot
Iterative Procedures, S.D. Thesis, Department of
Nuclear Engineering, MiT, June, 1959.
(4)
(5)
Westcott, . H, "Efective Cross Section Values for WellModerated Thermal Reactor Spectra," (3rd edition corrected)
AECL-1101l July, 1962.
"Douglas Point Nuclear Generating Station," Atomic Energy
of Canada Limited, AECL-1596.
(6)
Francel, &., "Convergence Rates of Iterative Treatments of
Partial Differential Equations," Math* Tables Othet
Aide to Computation, , 1950, p. 65.
(7)
Young, D. No, "Iterative Methods for Solving Partial
Differential Equations of Elliptic Type," Doctoral Oisertation,. Harvard University, 15. Tran. Azer. Math. S00., '
p. 92.
(81
Sangren3 Ward D.
"Digital Computers and Nuclear Readtor
Calculations," J. Wiley and Sons, Inc., New
York,
i460.
(9) Hurat, D. G., and Henderson, W. 0., "The Effect of Flux
Flattening on thae Economics of Heavy Water Moderated
Rea ctors, AECL-949, Deoembet, 1959.
3