Note: Descriptions are shown in the official language in which they were submitted.
; - "" 11074Q9
Field of Invention
The present invention relates to fuel management
for pressurized water nuclear reactors, and in particular
to the arrangement of nuclear fuel assemblies within a
reactor core.
Brief Description of the Drawings
. Figure 1 shows two prior art in-core fuel management
schemes for a core having 241 assembly locations. The upper
- left quadrant (a) shows one symmetric quadrant of an OI scheme
'J 10 and the lower right quadrant (b) shows a symmetric quadrant
of an IOI scheme.
Figure 2(a) shows a symmetric quadrant embodying the
present invention in a manner that facilitates comparison
with the prior art shown in Figure 1, and Figure 2(b) shows
a schematic identifying the inner and outer region and the
checkerboard components thereof.
Figure 3 shows a typical prior art OI scheme for the
first cycle of a core having a total of 241 assembly locations.
Figure 4 shows the present invention in a second cycle
scheme that immediately follows the first cycle scheme shown
in Figure 3.
Figure 5 shows a schematic fuel assembly having a
16 x 16 fuel lattice, 5 water holes, and 8 lattice shims.
Figure 6 shows a typical relationship between the
power fraction in the inner region of the core and the difference
in K infinite between the outer and inner regions.
Figure 7 shows the present invention in a first cycle
scheme for a core having 217 assembly locations.
Figure 8 shows the present invention in a later cycle
3Q for a core having 217 assembly locations.
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- Figure 9 shows the present invention in a second cycle
fractional batch (z=2.62) scheme that immediately follows the
f irst cycle scheme shown in Figure 3.
Figure 10 shows the present invention in a third
cycle fractional batch scheme that immediately follows the
scheme shown in Figure 9.
Background of the Invention
Modern commercial nuclear power reactors are fueled
with uranium having a slightly enriched U-235 content, which
necessitates that portions of the core be periodically removed
and replaced with fresher fuel. The plan of replacement and
arrangement of fuel during the life of the reactor, known
as in-core fuel management, is a major design consideration,
having both safety and economic consequences. In a typical
pressurized water nuclear power reactor (PWR), the initial
core loading consists o~ three approximately equal sized
batches of fuel assemblies having different enrichments. In
conventional terminology, batch A has the lowest enrichment,
batch B a higher enrichment, and batch C the highest enrich-
ment. At the end of the first cycle, typically one year inlength, batch A is removed from the reactor, batches B and C
are rearranged, and a feed batch D of fresh fuel is placed
in the reactor. This procedure is typical of three hatch
in-core fuel management wherein an entire batch of fuel is
: removed and replaced with the same number of feed fuel assemblies
eyery year for the life of the plant. It is usually desirable
to achieve an equilibrium in-core fuel management scheme as
; early as possible in the plant lifetime, such that the feed
; assemblies will always haye the same enrichment and will be
placed in the same locations as the previous feed assemblies,
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and the once-burned and twice-burned assemblies that remain
in the core will be shuffled to identical locations occupied .
by the previously once and twice-burned assemblies.
Having introduced the nature of the art to which the
invention per~ains, and before proceeding to a more detailed
description of the background of the invention, a review of
the terminology commonly used in the art of nuclear reactor
fuel management will be
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i presented with a view towards defining the terms for specific use
. . . . .
herein.
A fuel assembly is a square array of fuel rods connected
at their ends by end fittings to form a unit that is insertable and
s removable from the core. Other structure that remains fixed ~ith ~-
respect to the fuel rods and end fittings during a particular cycle
is also considered part of the fuel assembly. The fuel lattice
within the assembly is the array of fuel rod locations of the
, ~
assembly, excluding water holes. Water holes are locations in the
;~ ; iO ~ fuel assembly where fuel rods are intentionally omitted, usually
~ in order to provide space forinstrumentation or for a control rod
.: ~
guide tube. These tubes are part of the structural support of the
assembly and provide guides wherein control rods may be reciprocated.
~ Fixed~burnable poison shims are solid material in the fuel assembly
,' 15 containing parasit~c neutron absorbing poison having a concentration
I; ~ which permits most or all of the poison to be consumed during one or
,':r,~ more cycles in the reactor. The enrichment of the fuel rods relates
to the fissile isotope content at the time of first introductlon
into the reactor core, i.e., when it is fresh, or feed, fuel.
.: :
~ A batch is d group of fuel assemblies that are placed
into, and~then permanently removed from, the core together. A
ot~i;s a group of fuel assemblies that are placed into the core
at the same time~, but which may or may not be permanently removed
at the same time. A cycle is the time during which the arrangement
.,, ~
;25 of fuel in the reactor core is unchanged, usually beginning with
the plscement of a feed batch or lot of fresh fuel into the care,
and ending with the removal of highly burned assemblies. Typical
cycles range from 10 to 15 months in duration. The number of burns
an individual fuel assembly or a lot of fuel has experienced is the
number of cycles it has been in the reactor core.
~ ~ A checkerboard is a pattern, superimposed on a grid region
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- of adjacent parallel rows and columns of uniformly spaced squares,
- that is similar to the red and black color pattern that appears on
the checkers game board. A checkerboard is characterized in that
. a line drawn through the diagonal of a single red square will, ifextended in either direction throughout the region, intersect only
~;~ red squares, and similarly for the black squares. In the present` context, checkerboarding fuel assemblies in the reactor core means that
. . .
one type or types of assemblies correspond to the red component
squares on the game board, and other types of assemblies correspond
`~`
to the black component squares on the board. The core periphery `
consists of the fuel assembly locations in the core where more than
~; a mere corner of a fuel assembly borders on the neutron reflector
jr i ~
~ at the outer boundary of the core.
... . . .
` ~ It is a primary purpose of in-core fuel management to
minimize the amount of U-235 or other fissile material required for
a given energy output during a given cycle. This can be appreciated
;1 ~ by the~rule of thumb that for every 0.1 effective weight percent
(wt~ ) increase in requ1red core average enrichment, the increased
cost of fuel for that cycle is over 2 million dollars. Typical
20 ~ ~equi;l~ibrium~cycle core average enrichments are about 3.3 wt% U-235.
It can~also be appreciated that the greatest savings in overall fuel
~ ~ ,
costs w11~1 be achieved by minimizing the feed enrichment required for
an equilibrium fuel management scheme.
The major constraint on the flexibility of in-core fuel
management is imposed by very strict power distribution limitations
,t ~
required by safety considerations. For example, the predicted
;` ratio of the powers produced in the hottest fuel rod to the core
average fuel rod is typically not permitted to exceed l.40. This
,~ imposes correlative requirements on the ratio of power produced in
a fuel assembly to the core average assembly power, and on the
- maximum rod power within an assembly to the average power in the
0290- - 4 -
)74(~9
assembly containing that rod. In modern commercial PWR's, fixed
burnable poison shims are ~requently located in selected assemblies
to control the power distr;bution. These shims are strongly
absorbent when the assembly is first placed in the core, and become
S weaker the longer they are exposed to the operating core environ-
ment. Although the shims are useful for controlling the power
distribution and other core characteristics such as the moderator
temperature coefficient, the presence of residual shim poison at the
end of a cycle presents an inherent reactivity penalty, and requires
a greater initial U-235 enrichment (and cost) at the beginning of
each cycle in order to overcome the parasitic neutron absorbing
effect of the residual.
l ~ The use of shims as a power shaping means has traditionally
i, been directed primarily to controlling the power distribution within
A I
and between assemblies, but the use of significant numbers of shims
will also affect the gross power shape in the reactor. This has
economic consequences in that a power shape that is peaked radially
toward~the center of the core will be more efficient in conserving
neutrons within the reactor so that they may produce additional
~ .,,
~fissions, than a power shape that is peaked near the core periphery,
where neutrons will leak out of the reactor and never return. Thus,
for the~same core average initial enrichment (and assuming zero end
, ; of cycle shim~residual), a longer cycle can be achieved when the
; ~ power shape near end of cycle is centrally peaked than when it is more
uniform or peripherally peaked.
Figure 1 symbolically shows two of the most common prior
art fuel management techniques implemented in a core having 241
fuel assembly locations. Each is a three batch second cycle scheme
:.,
; ~ for achieving the same power level and cycle length, but the
arrangement of the fuel types is characteristic of the respective
schemes in other cycles. The highly reactive feed fuel (D) is shown
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as crosshatched squares 10, 10', the less reactive once^burned (C)
fuel as open squares 12, and the least reactive once-burned (B)
fuel as crossed squares 14. Note that in a first cycle all batches
A, B, and C, would be fresh, but the different enrichments could be
represented by the three symbols, and in cycles after the second
the crossed squares 14 would represent twice-burned fuel.
In order to facllitate a later description of cycle-
independent fuel management, fuel loadings wi11 be designated by
their relative lots. Thus, lot L is the feed or fresh lot 10, 10',
L-1 the previously loaded fresh fuel 12, L-2 the next previously
loaded fresh fuel 14, etc., except that in the first cycle L, L-l,
and L-2 correspond to the customary C, B, and A lots, respectively,
and in second cycle L, L-l, L-2, L-3 correspond to D, C, B, and A,
respectively. In equilibrium cycles, the numerical portion N of
the L-N designation can be thought of as the number of cycles the
lot has previously resided in the core, i.e. the number of burns it
has experienced.
The upper left quadrant (a) of Figure 1 shows what is
commonly referred to as the Out-In (OI) prior art fuel management
scheme. This is characterized by unshimmed feed (L) fuel 10 placed
at the core periphery to the extent possible. Any feed assemblies
; that are left over are located towards the periphery and surrounded
to the extent possible by twice-burned (L-2) fuel 14. In the next
cycle, the feed fuel will have become once-burned (L-l) fuel 12, and
as shown in (a), the once-burned fuel 12 is concentrated in the core
center. In general, the OI scheme has an inner region of once-burned
fuel 12, a peripheral region of feed fuel 10, and an intermediate
region of primarily twice-burned 14 mixed with some feed 10 and
once-burned 12 fuel. It is noted that this concept for arranging
fuel has also been used in first cycle designs.
The OI fuel management has the advantage of providing
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7409
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a relatively flat cosine gross core radial power shape, which helps
avoid excessive local peaking. But as the fuel is depleted during
the cycle, the gross power tends to shift towards the core periphery
where the fresh fuel is located. The relatively high peripheral
,~ ~ 5 power, however, produces a high neutron leakage, especially at end
of cycle (EOC) when the interior of the core has been depleted and the
.. ~ - .
exterior is still relatively highly reactive.
A prior art attempt to improve the neutron economy and
reduce the required enr~chment of the OI scheme is shown in (b) of
10- ~ Figure 1, which will be referred to as the In-Out-In (IOI) scheme.
,, In this scheme, all feed (L) assemblies 10' contain burnable
~ poison sh1ms (represented by c1rcles) and are placed towards the
;i ~ center of the core in a checkerboard pattern that alternates components
~of L assemblies lO' with components of twice-burned (L-2) assemblies
lS ~ 14. The L component is violated near the core center (assembly
locations~ 50, 58) in order to accommodate the well known tendency of
r j
I ~ the power distribution to peak in this area. All once-burned (L-l)
i
fuel 12 i~s placed as far as possible towards the core periphery.
Thus,~the IOI~scheme is characterized by an inner checkerboard of
~feed fuel~and twice-burned fuel and an outer region of once-burned
:, 1 : : : -
fuei. The IOI scheme as practiced in the prior art requires that
the~shims in the feed fuel assemblies be removed after one cycle.
The~101~scheme thus places fresh shimmed fuel in the center region,
then removes the shims at the end of the cycle so that at the
'~25~ ~ hginning of the next cycle the once-burned fuel contains no shims.
$; ~ Since the twice-burned fuel was previously a once-burned fuel, it
; also contains no shims.
~ The major advantage of the IOI scheme is the low neutron
, ~ .
leakage from the core periphery resulting from the tendency of the
power distribution to remain centrally peaked throughout the burnup
cycle. In addition to permitting a lower initial enrichment for the
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same energy extraction, the centrally peaked power distribution
produces a lower radiation exposure to the reactor internals and
vessels surrounding the core, and has other advantages related
to the stability of the power distribution.
^ 5 The prior art requirement in the IOI scheme that the
`~ shims be removed at the end of the first`cycle of exposure of the
feed assemblies has an inherent disadvantage which limits the
x~l~; flexibility of fuel management. The purpose of shimming the feed
fuel is to control the power shape so that the fresh fuel in the
central region of the core will not produce power too great in
relation to the core average power. This control requlres such a
,~.
high initial concentration of poison material in the shims that the
, ~ poison does not burn out by EOC and therefore a significant parasitic
,~ effect remains. Nevertheless, the advantage of the lower neutron
3. 15 leakage from the periphery is greater than the disadvantage at end
` i cycle of having a significant posion shim residual. By removing
these shims prior to the next cycle, the parasitic shim effect is
:^ not carried over into the next cycle. In order for the shims tobe eas1ly removed, however, they are placed in guide tubes normally
~; 20 ~ ~reserved~for control rods rather than being permanently integrated
; in the~;fuel lattice. This precludes the placement of feed assemblies
under control rods in the IOI scheme, and thus eliminates one-third
.,,: . ~
or more core locations from use with feed assemblies. Such loss of
fuel piacement flexibility can be particularly res~i ctive if the
energy extraction or cycle length 1s to be varied from equilibrium
; ~ ~ IOI values. In order to best accommodate a non-equilibrium cycle
^ ~ or to optimize the return to equilibrium, fresh fuel might well be
.: ~
- ideally placed in some of these locations yet cannot be without
~ - abandoning the prior art IOI scheme. In addition, the limited
. ~
flexibility of the IOI scheme is even more evident if the scheme
is used in cores employing more advanced control rod designs wherein
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up to twelve control rod fingers are insertable into five adjacent
assemblies by the action of a single drive mechanism. These control
` rods permit greater reactivity control and offer other significant - :
advantages, yet are generally impossible to use in cores having
many of the control rod guide tubes occupied for other purposes,
as in the IOI scheme.
If the prior art IOI scheme is modified so that the shims
are left in each feed assembly at the end of cycle C and not removed
when the assembly is shuffled into a once-burned location on the
- 10 core periphery in cycle C+l, the residual shim absorption near the
periphery will tend to accentuate the power near the core center,
requiring that the cycle C+l feed batch have even stronger shims to
`i control the power peak at the beginning of cycle C+l. The fresh
fuel will than have an even greater shim residual at the end of cycle
C+l and, when this fuel is placed on the periphery in cycle C~2
the peripheral power will be even further depressed requiring even
stronger init~al shim loadings on the next batch of feed fuel. The
end of cycle residual thus would become so large as to dissipate
: . ,
~ the advantage in the IOI scheme of low neutron leakage.
.. . .
~ 20 Summary of the Invention
: .,i
t is an object of the present invention to reduce the
required core enrichment relative to the prior art OI fuel management,
and to increase fuel placement flexibility relative to the prior
art IOI fuel management, without exceeding acceptable power distribution
limits. It is another object to achieve this improvement without the
necessity of removing shims from the assemblies.
... ~
The present invention exhibits the major benefits of
the two important prior art PWR fuel management schemes, yet it is
; ~ independent of them. The invention is an in-core fuel management
scheme for a PWR core wherein the arrangement of fuel assemblies
`: :
n resulting from satisfying certain empirical reactivity relationships
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.; among assemblies can be characterized by reference to an imaginary
. ~ . .
boundary between a radially inner region containing about two-thirds
~; of the assemblies in the core and a radially outer region containing
the remainder of the assemblies. The inner region comprises a
~ 5 checkerboard pattern of fuel assemblies in which feed (L) assemblies
`~ ~ and once burned (L-l) assemblies occupy at least two-thirds of one
~-~ component of the checkerboard, and once or greater burned (L-l, L-2,
.
L-3,,..L-N) assemblies occupy the other comPonent. At least some of
the feed assemblies in the inner region contain fixed lumped burnable
, 10 poison shims.
;,``~ In the ideal embodiment, the first component of the inner
` checkerboard consists entirely of shimmed L assemblies and L-l as-
'~:
; semblies, and the second component comprises twice or greater burned
assemblies. The outer region is characterized by another checkerboard
"
pattern, one component of which consists entirely of feed (L)
assemblies and the other component of once and higher burned (L-l,
L-2,.. L-N) assemblies. The feed (L) component on the outer region
~ ~ need not match the feed and once-burned component of the checkerboard
; ~ in the inner region.
When used for the first cycle of operation, where all fuel
; os~semblies are unburned, the highest enrichment (batch C) corresponds
to the feed (L) assemblies and the next highest enrichment (batch B)
::
corresponds to the once-burned (L-l) assemblies. The invention may
thus be used in any cycle of reactor operation and with any refueling
, .,
` ~ 25 schedule.
~ : ~
i ~ ~ The present invention offers typical core average enrichment
savings relative to the prior art 0I schemes of over 0.1 wt% in
, .. . ~
~ ~ equilibrium cycles, 0.2 wtX in second cycle, and about 0.05 wt% in
:~ first cycle. In addition, the invention permits the shims to remain
~ 30 in place in the assemblies throughout their lifetimes in the core,
`- without restricting the placement of the assemblies under control rods.
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The advantage of the invention over the IOI scheme is
achieved by eliminating the requirement for a sizable poison
residual to suppress the power in the feed (L) assemblies at
the end of cycle. Therefore, the shims can be initially weak
~ enough to allow the poison material to burn out to essentially
''
zero shim residual during the first cycle they are in the core.
In the prior art IOI, the high shim worth is needed at beginning
and end of cycle to control the centrally peaked power distri-
~,
bution caused by the concentration of fresh fuel in the central
region. By replacing some of the feed assemblies with once-
burned fuel, the invention places slightly less reactive (L-l)
assemblies in the feed fuel component of the inner checkerboard,
thereby reducing the inherent reactivity of the central region
of the core relative to a completely filled feed fuel com-
ponent. Thus, the inherent tendency for central power peaking
at beginning and end of cycle is lower than in the IOI scheme,
and the need for control of this central power with poison shims
is also reduced. With the present invention, the shim worth
residual at the end of cycle is low enough, less than 0.5
2Q percent K, to have only a slight effect on the power distribu-
tlon at the beginning of the next cycle. Therefore, the feed
fuel in the next crcle does not require excessively strong
shims in order to compensate for the residual remaining in
the L-l assemblies, as would be the case in the IOI scheme if
the shims in the L assemfilies were not removed prior to the
start of the next cycle when the previous-ly fresh fuel assem-
blies become L-l as-semfilies.
In accordance with the invention there is provided
in a pressurized water nuclear reactor having a multiplicity
of elongated, square fuel assemblies forming a generally
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cylindrical core which must be periodically refueled between
..:
burnup cycles by removing a fraction of burned assemblies,
rearranging the remaining burned assemblies, and inserting
fresh assemblies, each assem~ly belonging to one of lots L,
L-l, L-2,...L-N, depending on whether the assembly resided
in the core for 0, l, 2,...or N previous burnup cycles respect-
ively, the arrangement of assemblies to begin a new burnup
cycle after refueling, comprising: (a) a generally cylindrical
inner core region consisting of approximately two-thirds the
total assemblies in the core and forming a figurative checker-
board array having (1) a first checkerboard component at least
two-thirds of which consists of fresh assemblies (from lot L)
and assemblies (from lot L-l) having burned through only one
previous burnup cycle, at least some of the fresh assemblies
containing fixed burnable poison shims, and (2) a second
checkerboard component consisting of assemblies (~rom lots
L-l, L-2...L-N) having burned through at least one previous
burnup cycle; and (b) a generally annular outer region consist-
ing of the remaining assemhlies and included at least some
fresh assemblies.
Description of the Preferred Embodiment
As set forth in the Background of the Invention, in-
core fuel management is a very important feature of nuclear
power plant design. Therefore, much time and money is spent
by nuclear reactor vendors to optimize the fuel management
for each particular reactor through the use of detailed com-
puter simulation prior to fuel fabrication. All data pre-
sented in the following description of the invention were
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.1074~9
generated in the course of a computer simulated verification that the
inventive concept would indeed satisfy the above-recited objectives
of the invention. The calculational models for implementing the
~` invention are well-known in the art of nuclear reactor fuel management,
and the following description usedln conjunction therewith will enable
one ordinarily skilled in this art to adapt the invention for use in
any size PWR for any fuel cycle requirements ordinarily desired for
large electric power generating stations.
In one embodiment,the invention is implemented in a reactor
core that has previously been loaded with fuel for one or more cycles
accordlng to some prior art scheme. Such an embodiment is illustrated
in~ Figures 2(a) and 4, where a second cycle embodying the invention
immediately follows the prior art OI first cycle shown in Figure 3.
The following table, used in conjunction with Figure 3, summarizes
the important fuel design properties of the OI first cycle, and will
serve as a reproducible starting point for practicing the embodiment
of the invention described hereinbelow.
Table 1
; Fuel Design for First Cycle
Prior Art Out-In Scheme
Shown in Figure 3
Assembly No. Shims in No. Assemblies Enrichment No. Fuel Shim
Type Assembly (wt% U-235)Rods Loading
(wt% B4C in
B4C-A1 203 )
A 0 81 1.83 19116
BL 16 36 2.49 7920 2.76
~ BH 16 52 2.49 11440 3 37
;~ CL 16 24 2.95 5280 2 04
CH 16 8 2 95 1760 3.37
C 0 40 2 95 9440
In Figure 3, the numeral 16 in the upper left corner of each
` assembly identifies an assembly location. Location number 69 is atthe core center, and the parts of the core not shown and the fuel
contained therein are merely reflections along the major axes. A
schématic of a typical fuel assembly 18 is shown in Figure 5, where
fuel rods 20, fixed burnable poison lattice shims 22, water holes 24,
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nd guide tubes 26 (one sho~n) are represented. More details of the
ore and fuel assembly designs can be found in the Combustion En-
gineering Standard Safety Analysis Report ~CESSAR)'Docket No. STN-
' 50-470 Section 4.3 (1975). " '
~ 5 In order to more clearly compare and distinguish the
; invention from the prior art, Figures l(a) and l(b) show how the
prior art would be used to design a second cycle following the same
13,800 MWD/T first cycle shown in Figure 3. In the OI prior art
second cycle scheme shown in Figure l(a), the A assemblies are
. ~ 10 removed (except that the most reactive A assembly is moved to the
co~re center), the B fuel 14 and C assemblies 12 relocated as shown,
~ and unshi~med D assemblies 10 having an average enrichment of 3.50
`~ wt70 are inserted. The beginning of cycle 2 (BOC2) core average
initial enrichment is 2.97 wt~o, sufficient for a second cycle burnup
15~ ~ ¦ of 10,000 MWD/T.. In the IOI cycle 2 pri'or art scheme shown in
,,, ~
Figure l(b), the D assemblies 10' are shimmed and have an average
enrichment of about 2.96 wt,~. The core average BOC2 enrichment is
about 2.75 wt% for the same energy extraction as the OI scheme.
The second cycle scheme e~bodying the present invention
~is~shown in Figures 2(a) and 4. The inventive concept contained
therein is derived from the discovery that the inner checkerboard
in~the IOI~scheme of Figure l(b), which has one component of feed
fuel 10 (L) and another component of B (L-2) fuel 14, can be sig-
nificantly violated yet give an overall improvement in the gross
.,
power distribution and a decrease in the required shim worth, by
an interchange of feed (L) fuel 10 and C (L-l) fuel 12 according
:
~' ~ to a general procedure to be described below. The resulting ne~J
; in-core fuel management s~heme can'be characterized by reference
to an imaginary'boundary 28 between an inner region 30 containing
about two-thirds of the assemblies and an outer regi-on 32 as shown
in Figures 2(a) and 2(b). The recbmmended outer boundary of the
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inner region consists of all assemblies intersected by a circle
` drawn about the core center, havlng a radius equal to three-quarters
the distance from the core center to the closest point on the outer
` edge ofthe core periphery. In Figure 2(b), the distance to the
s periphery is labeled P and the boundary circle radius is labeled R.
`~ The following table summarizes the feed fuel assembly
properties represented in Flgure 4. The numeral 34 in Figure 4
indicates the previous location of the A, B, and C assemblies.
The numeral 36 in the lower rîght corner of the D assemblies in- -
dicates the type of shim loadings and distrlbution resulting from
~ ~:
application of the method to be described below.
Table 2
Feed Fuel Design for Second Cycle
Using the Invention
As Shown in Fi~ure 4
~ Assembly No. Shims No. of Enrichment Shim Loading
; 15 Type per Assembly Assemblies
D401 0 32 3.28 O
D*402 8 16 3.01 1.59
D*403 4 8 3.01 1.82
D~404 8 8 3.01 1.87
~D*405 8 4 3.01 2.21
D*406 8 8 3.01 1.99
D*A07 4 4 3.01 3.12
The following is a detailed description of the method
of implementing the invention. The intent is to satisfy certain
reactivity and power relationships at the beginning of each cycle,
which have~been found to consistently produce, particularly at EOC,
the advantages of the invention as described above. This method
25 instructs one to arrange fuel at BOC by first determining what the
limiting K infinite (hereinafter K) balance in the core can be at
ÉOC and still satisfy the local fuel rod peaking limits, then working
i. .
~`; back to the feed assembly enrichment, shim strength, and placement
that will, with burnup, come within the EOC K balance. The steps
30 in the method are based more on the characteristics of the core and
. fuel assembly design than on the specific fuel management scheme used
. .
0290 - 15 -
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` l~V~409
~ ~ the prior cycle. Thus, one familiar with the basic core and fuel
.
~` assembly characteristic of a particular reactor in which prior art
fuel management techniques have been used, can with relatively little
effort implement the present invention.
First, the core geometry is divided into an inner region
; which cohtains approximately two-thirds of the assemblies, and an
-`~ outer region containing the remainder of the assemblies. A rec-
ommended boun~ary between the regions is a circle about the core
; center having a radius equal to three-quarters the shortest distance
from the core center to the core periphery. From previous, commonly
~ available calculations, the ratio of the hottest fuel rod in the
; inner région 30 to the average rod in the inner region is determined.
- This ratio, Pi/Fi, is preferably obtained from existing fuel
~ .
; ~ management schemes which use the present invention or the IOI tech-
n1que, but OI power distributions~can be used if the calculated ratio
is augmented by the ratio of power of an EOC feed assembly to the
power of an adjacent EOC twice-burned assembly. This augmentation
factor can be determined from a checkerboard calculation having typical
; ~ end of cycle fuel characteristics.
The next step is to determine the relationship at EOC of
~, the~difference in K between the outer region 32 and the inner region
,, ~
30~(QKo j), and the resulting ratio of the average power in the inner
region to the core average power, Pi/P. Figure 6 shows this relation-
ship for the 241 assembly and the 217 assembly cores shown in various
. , : .
other figures, where the basic fuel assembly design shown in Figure
5 is employed. This relationship is determined from surveying several
end of cycle power distributions from any fuel management scheme
i ,. . .
wherein the absorption of all shim poison material is cancelled from
the calculation so as to represent zero shim residual.
`
The designer then chooses the design target axially
integrated radial peak fuel rod to core average rod power ratio,
:
290 . - - 1 6 -
.
- . . -
.~ . ~ . . ..
1~7~9
`~ commonly known as Fr~ a value usually imposed on the designer as a
, consequence of safety considerations. By dividing Fr by the ratio,~ Pi/Pi, the maximum permitted value of Pi/P consistent with the design
; , target Fr iscbtained. In the present example, Fr is 1.41 and Pi/P,~; 5 is 1.28. The required division indicates a permitted inner regionpower ratio Fi/p of about 1.10. Referring again to Figure 6, it can
be seen that the end of cycle difference ~ _j(EOC) required to produce
a P~/P equal to 1.10 is 9.2%.
In order to obta~n the same K difference at beginning ofl ~ 10 ~ cycle QKo-i(Boc) to assure an Fr less than,1.41 based on the dif-
ference;in K determined immediately above QKo j(EOC), a correction
must~be made for the difference in regionwise exposure between end
of cycle and beginning of cycle. The first step is the determination
of~the difference in accumulated exposure between the inner and outer
'15~ ~ regions over the cycle. This difference is just (Pi/F - Fo/p) *
CYCLE LENGTH. In the present example where Fi/~ is 1.1, Po/P for the
outer one-third core is 0.8, ahd for a cycle length of 10,000 MWD/MTU,
the~inner;region accumulates an additional 3,000 MWD/MTU relative to
the outer~region. This difference between inner and outer region
20~ ~ exposure is converted into a reactivity difference according to well-
known deriva~t~ves of the change in core K with exposure. In the
;present~exampie~, the adjusted reactivity difference (unshimmed) at
BOC2 is ~about 6.5%. This BOC2'~K must be further adjusted to account
for~the;shim residual poison carried over from the EOCl batch B and
~. ~
r~ 25~ a few C fuel assemblies. This EOCl shim residual poison is depleted
...,.
; during the course of cycle 2 and does not contribute to the difference
' ~ in regionwise K at the EOC 2. The adjusted reactivity difference
~ , at BOC2, allowing for the shim residual carried over from cycle 1, îs
'ç,''~ about 7.5% ~ K. As will be described below, the difference between
this BOC2 value and the EOC2 regionwise reactivity difference of 9.2%
; .,
', ~K is accounted for in the design through the placement of shims in
~i290 ~! l 7
. .
.
11074(~9
`::
~ the fresh assemblies. It is the latter reactivity difference, of 9.2%
- ~K, that the designer strives for an order not to exceed a peak
- fuel rod power Fr of 1.41. Experience shows that in a scheme arranged
-` with the present method, the absolute value of the peak and the region-
- 5 wise power density PilP remain fairly constant throughout the burnup
. ,
~ cycle.
. :i
The next step is to make a rough estimate of the required
fresh feed enrichment in the D-batch, which can be obtained by taking
, ; the core average initial enrichment required to produce the desired
lO ~ second~cycle length using the IOI scheme and adding about O.lS wt%,
, :
or us1ng~the OI scheme and subtracting about 0.4 wt%. In the present
example, the D feed enr~chment is about 3.12 wt%, and the beginning
. 7~ BOC2 core average enrichment is about 2.85 wt%.
At this point, the following target characteristics have
'.` I ~
15~ ~ been estimated for BOC2~: the reactivity difference between the outer
and~inner regions (9.2X), the amount of this reactivity difference
that should be distributed as shims in the fresh assemblies in the
inner region (1.7%), and the average enrichment of the fresh fuel
(3.~12~wt~ It remains to choose the specific shim loadings (boron
, i - .
~ content)for the fresh assemblies, and to arrange all the assemblies
in~the reactor core.
This can be facilitated by performing a few preliminary
tr1al and error hand calculations of ~Ko j(BOC) based on known values
of~K for each fuel assembly in the core at BOC2. The assemblywise
25 ~ K's can be obtained by performing a single core reactivity calculation
; at the estimated BOC2 so1uble boron concentration with noxenon
and peak samarium in the burned (L-l, L-2,...L-N) assemblies. Fresh
assemblies having a variety of shim loadings are included in this
,::
~!1 calculation, so that a relation between K and shim loading is deter-
~ 30 mined. The adequacy of specific shim loadings and fuel assembly
-~ arrangements can be estimated through trial and error according to
3290 - - 18 -
. ~
.. - : ... . . .
- .. . . .
.,. . . . : ' . , ' :
107409
; the following plan.
The inner region of the core is filled with a quarter
core symmetric checkerboard having one component of L and a second
component of L-2 assemblies. L-l assemblies are placed toward the
core periphery. An arithmetic reactivity difference is calculated
between the outer and inner regions of the core, which will generally
be smaller than the target ~Ko j(BOC). Shims are located in L
assemblies such that the inner region contains about 2.7% more shim
worth than the outer region(l.7% in fresh assemblies and 1.0% carry-
.;
over from first cycle). The inner region reactivity must be further
reduced, and this is accomplished through the key step of interchanging
L-l assemblies from the outer region with L assemblies from the inner
region. It will be generally found advantageous to place L assemblies
in several peripheral locations. The L-l and L assemblies are
~l 15 interchanged, and the shim loadings and placement are manipulated,
'$:'. until the hand calculation indicates the desired QKo j(BOC) (9.2%)
and the desired L assembly shim worth in the inner region (1.7%)
have been achieved. At thls point, customary computer calculations
, can be employed to fine-tu;ne the power distribution and to verify
,l~ 20 the estimated enrichment.
Figure 4 and Table 2 include information showing the resulting
change in location of the L-l and L-2 (and a single L-3) assemblies
from EOCl to BOC2. Also shown are the number of shims in each L
assembly and the shim loading in wt% of B4C (containing natural
boron) in B4C-AL203 shim material. The invention is not limited to
" ~ .
use with B4C shim material, however, and can be practiced, for example,
with lattice shims composed of an admixture of gadolinium and fuel
material (U02), or with removable shims whether or not located in
the guide tube. It is well within the skill of an ordinary nuclear
fuel management engineer to substitute other shim material, or other
fuel lattices, without departing from the scope of the invention.
~290 - 19 -
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110741~9
::.
It is to be understood that once the target BOC arithmetic
~Ko j difference is achieved, a computer calculation of the power
~ djstrjbution during the cycle is to be made. It is expected that
- several iterations in which minor adjustments of shim loadings,fuel enrichment, or fuel assembly placement are made may be needed
before satisfactory power distributions and EOC reactivity are
obtained. After practicing the present invention a few times,
however, one having ordinary skill will need only about two or
three such iterations.
Referring again to Figure 2(a) the differences in the
arrangement of fuel assemblies with the present embodiment of the
^~ invention can be identified relative to the arrangements of the prior
art OI scheme shown in Figure l(a) and the IOI scheme shown in
Figure l(b). With respect to the boundary between the inner and
outer region indicated by a heavy line 28, the present invention
consists of a checkerboard pattern in the inner region having one
component consisting of L (lO, lO') and L-l (12) assemblies and a
second component consisting of L-2 assemblies (14). The core
geometry of Figure 2(a) is shown in Figure 2(b) where first component
40 and second component 42 lines of the inner checkerboard and third
component 44 and fourth component 46 lines of the outer checkerboard
(to be later described) are indicated. The prior art does not show
; a checkerboard wherein the first component 40 consists mostly of~- L and L-l assemblies. In the embodiment shown, the second component
42 of the inner checkerboard consists entirely of L-2 fuel and, when
the center assembly is included, L-3 fuel.
It is also seen that the outer region 32 consists of a
checkerboard of L assemblies on the third component 44 alternating
with a fourth component 46 of L-l and L-2 assemblies. The OI scheme
of Figure l(a) intentionally avoids checkerboarding L fuel in the
outer region. There is no discernable checkerboard pattern in the
~2gO - 20 -
1~7409
outer region of the IOI scheme shown in Figure l~b), since adjacent
components of L-l fuel near the periphery have no L fuel.
With respect to the OI scheme of Figure l(a), none of the
L assemblies is shimmed, whereas in the present invention at least
some of the L assemblies 10' are shimmed. Furthermore, in the present
invention less than two-thirds of the L assemblies are in the outer
region, whereas in the OI scheme almost all L assemblies are in the
,~ outer region.
With respect to the IOI scheme shown in Figure l(b), no
L assemblies are on the core peripher~ whereas in the present
invention there are several L assemblies on the periphery. Further-
., ~
more, every L assembly 10' is shimmed in the IOI scheme, whereas
in the present invention the outer region includes at least some
.' unshimmed assemblies 10.
The abov~ comparison of the present invention with the prior
art is based on the preferred embodiment of the invention. As will
be described below, different fuel management objectives may require
.different relative fractions of L, L-l, L-2,.. L-N assemblies in the
core, and the cheskerboard components may therefore not be as
perfectly filled as in the present embodiment. Nevertheless, the
essential characteristic of the present invention, the first component
of the inner checkerboard consisting mostly of L and L-l fuel, is
found in all embodiments of the invention.
Figure 7 shows the invention practiced in the first cycle
j 25 of a core havlng 217 assembly locations. The core contains unshimmed
` A fuel 14, shimmed ~BS) 12' and unshimmed B fuel 12 and shimmed (CS)
; 10' and unshimmed C fuel 10. In this embodiment, the first component
40 of the inner region consists of L (10, 10') and L-l (12, 12')
assemblies, and the second component 42 consists of L-2 (14) assemblies.
In the outer region the third component 44 is chosen from L, L-l
assemblies and the fourth component 46 is chosen for L, L-l, and
L-2 assemblies. Although a few minor modifications are required to
290 - - 21 -
.
7409
:,
the outline of steps discussed previously for implementing the
inventive scheme, an ordinarily skilled nuclear reactor fuel manage-
ment engineer can easily adapt the above procedures for use in designing
the first cycle. For example, it is well known that in the first
; 5 cycle most or all of the B (L-l) as well as the C (L) assemblies
require substantial shim loadings.
Figure 8 shows a later cycle scheme in the 217 assembly
core in which the first component of the inner checkerboard contains
four L-2 assemblies in each quadrant (assembly locations 16, 23, 43
and 51). This deviation from a perfect L and L-l first component
is sometimes the best way to accommodate peculiarities of the core
power distribution in which certain assembly locations exhibit
high power peaks. It is believed that a minimum of two-thirds of
the first component locations must contain L and L-l assemblies, and
that at teast one-third of all L assemblies be in the inner region,
in order not to depart from the inventive concept. It is noted
; that it may not be necessary to use shims in every L assembly
of the first component, especially if several different enrichments
are used in each batch. This would permlt concentrating the
desired shim worth in only a few L assemblies in the inner region.
Although such an arrangement falls within the scope of the invention,
it is believed that the power distribution cannot be controlled if
more than one-third of the L assemblies in the inner region are un-
shimmed.
Referring now to Figures 9, and 10, there is shown an
; application of the present invention in the 241 assembly core designed
for fractional batch fuel cycles. In fractional batch management, the
distinction between a lot of fuel and a batch of fuel becomes im-
portant. In the normal three batch fuel management, a batch and a
lot are synonymous because all the assemblies in a batch remain in
the core for the same number of cycles and are removed together.
,'~
J2~0 - 2~ -
' ' -: . '
~1~)7409
In the fractional batch scheme shown in Figures 9, and 10.
some assèmblies of a batch are removed while others remain in the
i core for the next cycle. For example, in the third cycle fractional
batch scheme shown in Figure 107 the L or feed lot, 10, 10' contains
-~ S 92 assemblies, the L-l lot 12 contains 92 assemblies, and the L-2
1 lot 14 contains only 57 assemblies. This means that before the L-l
,"~ assemblies are shuffled for the next cycle, 35 are permanently removed
from the reactor, leaving only 57 as L-2 assemblies.
In the second cycle shown in Figure 9, the first component
40 of the inner checkerboard consists of L and L-l assemblies, and
il the second component 42 consists of L-2 assemblies. In the outer
region, the third component 44 consists of L and L-l assemblies
and the fourth component 46 comprises assemblies chosen from lots
, L-l and L-2.
lS In the third cycle embodiment shown in Figure 10, the
first component 40 of the inner region checkerboard consists of L
and L-l assemblies, and the second component 42 consists of L-l and
L-2 assemblies. In the outer region checkerboard, the third com-
ponent 44 consists of L and L-l assemblies and the fourth component
46 consists of L-l assemblies.
It can be appreciated that, as fuel management schemes
become more tailored to the individual needs of particular utilities,
- the use of fractional batch fuel management will be more common.
~levertheless, the present invention finds application in such use
and the procedures outlined above for implementing the inventive
scheme can easily be adapted for use with the more complex schemes.
:
.:.
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