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Idealized Methods of Fuel and Poison Management
Zoned loading. By charging fuel of different enrichments to different zones in the reactor, or by using a different concentration of poison in different parts of the reactor, it is possible to change the power density distribution from the undesirably nonuniform cos J0 distribution to a distribution in which more of the reactor operates at the maximum permissible power density. One general type of zoned loading, which is close to optimum for a reactor in which the fuel linear power limits thermal output, is a reactor designed to have uniform power density throughout a substantial fraction of its core. This may be done by providing fuel in a central region, in which the flux is made uniform, of lower enrichment than in the peripheral regions of the reactor, the so-called buckled zones. A similar result may be obtained by poisoning fuel more heavily in the flattened central region than in the peripheral buckled zones. In addition to its advantage of providing more uniform power density, zoned loading also has the advantage of providing uniform bumup for at least the fuel in the part of the reactor where the flux is uniform. A disadvantage of zoned loading is the need to use in the buckled, unflattened zone fuel of higher enrichment, and hence greater cost, than would be necessary with uniform loading. The bumup of fuel in the buckled zone is also very nonuniform.
Partial batch replacement. Another method of fuel management, designed to deal with the nonuniform bumup of fuel, which is a second disadvantage of simple batch irradiation, is
partial replacement of the fuel at the end of life instead of complete replacement. In this method, at the end of life only the most highly burned fuel is replaced by fresh fuel, and the rest of the charge is left in the reactor until the next time fuel has to be replaced. An example of how this might be done is shown in Fig. 3.7, which represents a cross section of a reactor core containing 320 square fuel assemblies, such as might be used in a large boiling — or pressurized-water reactor. Fuel assemblies are divided into groups containing equal numbers, each in a roughly annular zone. In the example of Fig. 3.7, five zones, each containing 64 assemblies, are shown, with zone 1 farthest from the center and zone 5 at the center. In the method of partial batch replacement, all zones initially are charged with fuel of the same composition. As irradiation proceeds, fuel in the central zone 5 is burned at a higher rate than fuel in the outer zones, because the flux is highest at the center of a uniformly fueled reactor. When it becomes necessary to replace fuel, either because fuel in zone 5 has reached the maximum permissible burnup, or because the reactor is no longer critical, only the most highly burned fuel, in zone 5, is replaced by fresh fuel, and irradiation is continued. When it again becomes necessary to refuel, the fuel then most highly burned, which will now probably be in zone 4, is replaced by fresh fuel, and so on. The advantage of this method of fuel management, of course, is that the fuel discharged each time has fairly uniform composition, because it comes from parts of the reactor where the flux has been fairly uniform. Disadvantages are (1) the need to open the reactor more frequently for refueling than when all the fuel is replaced at the same time, and (2) the peaking in flux and power density that occurs whenever fresh fuel is charged to the center of the reactor with partially depleted fuel elsewhere in the reactor, as in the first refueling of the foregoing example.
Scatter refueling. Flux peaking can be reduced by a different method of partial batch replacement, called scatter refueling, which is illustrated by Fig. 3.8. In this method, fuel is
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Figure 3.8 Fuel pattern in scatter refueling. |
divided locally into groups containing the same number of assemblies, in this case into 80 groups each containing four assemblies. At the first refueling, an assembly in position 1 from each group is replaced by fresh fuel. At the second refueling, the assembly in position 2 from each group is replaced, at the third refueling the assembly from position 3 is replaced, and at the fourth refueling the assembly from position 4 is replaced. At the fifth refueling, each assembly from position 1 is replaced for the second time, and so on. After this stage is reached, at the beginning of every fueling cycle, each group of four assemblies will contain one fresh assembly, a second assembly that has been irradiated for one fueling cycle, a third that has been irradiated for two cycles, and a fourth that has been irradiated for three cycles. At the end of the fueling cycle, each group of four assemblies will contain one assembly that has been irradiated for one cycle, a second that has been irradiated for two, a third that has been irradiated for three, and a fourth that has been irradiated for four cycles and is then discharged and replaced by fresh fuel. The life of each assembly extends over four fueling cycles. When the individual assemblies are small, the neutron flux in each of the four assemblies of a group is nearly the same and flux peaking in the freshest, most reactive fuel is largely prevented. The overall flux distribution is flatter than in a uniformly fueled reactor, because the fuel in the center is more highly burned and less reactive than the fuel at the outside. Some power density peaking still occurs, however, because even though the flux is nearly uniform in a group of four assemblies, the freshest assembly has a higher fissile content than ones that have been in the reactor longer.
Scatter refueling also has two important advantages over simple batch irradiation: (1) Fuel of a given composition can be irradiated to a higher bumup before reactivity is lost in scatter refueling than in batch irradiation, and (2) less control poison is needed in scatter refueling than in simple batch irradiation. Both of these advantages of scatter refueling are a consequence of the fact that each part of the reactor contains some relatively fresh fuel and some fuel
nearing the end of life. The fresh fuel maintains reactivity, while the older fuel is giving up more heat than it could in simple batch irradiation without ceasing to be critical. Furthermore, in scatter refueling, the more depleted fuel that is present at all times acts as a control poison to absorb excess neutrons from the more reactive fresh fuel. Moreover, many of the neutrons absorbed by depleted fuel are used productively to make plutonium. These advantages of scatter refueling are a feature of all methods of partial fuel replacement.
These advantages of scatter refueling may be expressed somewhat more quantitatively by considering how the reactivity p of fuel changes with bumup B. To a fair approximation, reactivity decreases linearly with bumup:
p = p0-aB (3.1)
where p0 is the reactivity of fresh fuel. In simple batch irradiation, the bumup of fuel at the end of life, 51 when p = 0, is
5i = (3.2)
a
The amount of reactivity to be held down by control poison at the beginning of life, pi when В = 0, is
Pi — Po (3-3)
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To find the reactivity-limited burnup of fuel in и-zone scatter refueling, B„, note that at the end of life, the freshest nth fraction of fuel will have had burnup of approximately B„/n, the next older nth fraction 2Bn/n, etc., and the oldest nth fraction, ready for discharge, will have reached B„ bumup. The reactivity of this mixture of fuel is
But p = 0 at the end of life, so that
= 2np0 a(n + 1)
The ratio of the burnup obtainable in и-zone scatter refueling to that obtainable in simple batch irradiation is found by dividing Eq. (3.5) by (3.2):
in _ 2n Bl n + 1
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The reactivity of fuel in и-zone scatter refueling at the beginning of a cycle is
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By using (3.5),
The ratio of the reactivity change per cycle in n-zone scatter refueling to the amount in simple batch irradiation is
Pn _ ____ 2__
Pi n + 1
Values of these ratios for several values of n, the number of zones of assemblies, are tabulated below.
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Bumup ratio, scatter refueling/batch |
1.00 |
1.33 |
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1.67 |
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1.00 |
0.67 |
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1.00 |
0.67 |
0.50 |
0.40 |
0.33 |
0.00 |
Thus, four-zone refueling permits attainment of 60 percent more bumup than simple batch refueling, with only 40 percent as much poison needed to control reactivity changes. The time between successive fuel replacements is only 40 percent as long in four-zone refueling as in batch, however.
Graded refueling. These equations and table show that increasing the number of zones continues to improve bumup and reduce reactivity changes, until the bumup approaches twice that obtainable from batch irradiation, and the reactivity change approaches zero. It is not feasible to approach these limits in water-moderated reactors, because fuel assemblies are relatively large, and even the biggest reactors contain only a few hundred assemblies at most, so for the reactor to contain a reasonable number of groups, six assemblies per group is practically an upper limit. Moreover, these reactors have to be shut down and opened to replace fuel, and fueling interruptions would occur too frequently with much more than six assemblies per group.
Graphite-moderated, gas-cooled reactors, on the other hand, make use of thousands of fuel assemblies and are equipped with fueling machines that permit replacement of individual assemblies without interrupting reactor operation. In these reactors it is possible, therefore, to have a large number of assemblies per group and to refuel continuously during operation. Under these conditions, fuel within the reactor is graded almost continuously in composition from fresh unbumed fuel to fully burned fuel ready for replacement. The limiting continuous case of scatter refueling with n very large is sometimes called graded refueling. In graded fueling, when it is not necessary to shut down the reactor to refuel, it is possible to keep each assembly in the reactor until it has received the same bumup; whereas in scatter refueling, with a fixed fraction of fuel replaced at the same time, fuel removed from the center of the reactor is more heavily burned than fuel removed from the outside. Because the average composition and reactivity are constant in time, and all fuel discharged has the same composition, graded fueling is easier to treat analytically than scatter refueling with a finite number of assemblies per group, because of the changes in average composition and reactivity that then take place in each cycle.
Out-in refueling. Graded and scatter refueling have the disadvantage that the flux is higher in the center of the reactor than at the outside, although the nonuniformity is not so great as in simple batch irradiation because some highly burned fuel is always present at the center in graded and scatter refueling. An alternative method of fueling designed to depress the flux and power density further at the center of a reactor is out-in fueling. In this method, fuel is divided into annular zones of equal volume, such as those shown in Fig. 3.7. At the end of the first fueling cycle, fuel from central zone 5, the most heavily burned, is removed from the reactor; fuel from zone 4 is moved into zone 5; fuel from zone 3, to zone 4; fuel from zone 2, to zone 3; fuel from zone 1, to zone 2; and fresh fuel is charged to zone 1. At the end of each subsequent fueling cycle, this sequence of fuel movements is repeated. All cycles after the first few are similar, with the same cycle time, the same average burnup of discharged fuel, and the same change in reactivity. As fuel in the center of the reactor is most heavily depleted and least
reactive, the flux and power density are depressed there relative to a uniformly fueled reactor. The upper half of Fig. 3.9 shows the power density distribution calculated by Westinghouse [Dl] for three-zone out-in fueling of a 260-MWe PWR, with a core 1.25 m in radius operated at a burnup of 15,000 MWd/MT. The ratio of radial peak to average power density is 1.3, compared with about 1.5 for simple batch irradiation in this same reactor. The ratio of bumup with three-zone out-in fueling to bumup in batch fueling is about 1.5, as predicted by Eq. (3.6), which is approximately valid for this case also. Thus, out-in fueling has many advantages for a reactor of this size. ‘
For larger reactors with high burnup, however, out-in fueling leads to too great a depression in the flux and power density at the center of the reactor. This may be seen from the lower half of Fig. 3.9, which shows the power density calculated by Westinghouse [Dl ] for three-zone out-in fueling of a 1000-MWe PWR, with a core 6.5 ft in radius, operated at a burnup of 24,000 MWd/MT. At the beginning of a cycle, the flux peaks heavily in the outside zone, and the peak-to-average radial power density ratio is 2.0. The reason for this poor
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Center Outside
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Center Outside
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distribution is that the extra neutrons produced in the reactive outside zone 1, which are needed in the relatively unreactive central zone 3, must diffuse through a larger distance and hence require a greater flux difference than in a smaller core, with less reactivity difference.
Modified scatter refueling. For the largest reactors a combination of out-in and scatter refueling gives better results than either alone. Figure 3.10 shows how five-zone modified scatter refueling works. In this example for reactors with square fuel assemblies, fuel positions are divided into an outer zone 1 containing one-fifth of the fuel assemblies, and an inner zone containing the other four-fifths. Fuel in the inner zone is divided into groups of four for scatter refueling. At each refueling, the most heavily burned assembly in each group of four is removed from the inner zone and replaced by an assembly from the outer zone, which is moved in its entirety into the inner zone. Fresh fuel is then charged to the outer zone.
In this way the more depleted, less reactive inner zone is made to act rather like the flattened zone of zoned loading and the fresh fuel at the outside acts like the buckled zone. The peaking of power density at the center of a reactor using simple scatter refueling is reduced, without the overcompensation occurring with out-in fueling in a large reactor. The small reactivity change and high bumup obtainable with five-zone out-in or scatter refueling are realized.