To point to the importance of using improved methods of fuel and poison management, we shall discuss qualitatively the multiple drawbacks of the simplest method, which is batch irradiation of fuel initially uniform in composition, with spatially uniform distribution of boron control poison and with complete replacement of fuel at the end of its operating life. An example of this would be a PWR charged with fuel of uniform enrichment containing 4 percent 235 U and 96 percent 238 U and controlled by adjusting the concentration of boric acid dissolved in the water coolant to keep the reactor just critical at the desired power level. When this reactor starts operation, the compositions of fuel and poison are uniform throughout the core, and the flux and power density distribution are very nonuniform.

Figure 3.5 illustrates the spatial variation of power density in one-quarter of the core of a 1060-MWe PWR when the enrichment of 235 U and the concentration of boron control poison are uniform throughout the core. The lines plotted are lines of constant power density expressed as kilowatts of heat per liter of reactor volume, and also as kilowatts of heat per foot of fuel rod. The maximum permissible value of the latter is around 16 kW/ft, to ensure against overheating the fuel or cladding.

This figure illustrates immediately one of the disadvantages of batch fuel management. The power density, which is proportional to the product of the neutron flux and the fissile material concentration, is just as nonuniform as the neutron flux. If the local power density must be kept below some safe upper limit, to keep from overheating the fuel or cladding, only the fuel at the center of the reactor can be allowed to reach this power density, and fuel at all other points will be operating at much lower output. In a typical uniformly fueled and poisoned water-moderated reactor, the ratio of peak to average power density is over 3, so that the reactor puts out only one-third as much heat as it could if the power density were uniform.

The nonuniform flux is responsible for a second drawback of this method of fuel and poison management, the nonuniform change that takes place in fuel composition. In the center of the reactor, where the flux is highest, fuel composition changes more rapidly than at points nearer the outside of the reactor, where the flux is lower. As times goes on, therefore, the 233 U content at the center of the reactor becomes much lower and the burnup of the fuel much higher than toward the outside of the reactor. When the end of fuel life is reached, either because fuel at the center has reached the maximum bumup permitted because of radiation damage, or because the reactor has ceased to be critical with all boron removed, the outer fuel will have produced much less heat than the central fuel. If all fuel is discharged at end of life, the unit cost of heat from the outer fuel will be much higher than the central fuel. Figure 3.6 shows the final bumup distribution in a quarter of the core of a 1060-MWe PWR if charged initially with fuel of uniform composition.

A third drawback of this method of fueling is the large change in reactivity that takes place

between the beginning and end of fuel life. The reactivity of enriched uranium decreases steadily during irradiation. To compensate for this in simple batch irradiation, it is necessary to have a relatively large amount of control poison present at the beginning of fuel life and to withdraw this as irradiation progresses until at the end of life, ideally, all poison has been removed. When soluble poison such as boric acid is used, this means a high concentration at the beginning of life, with possible adverse effects on coolant corrosion and other chemical properties, and a large system for processing coolant to remove boron. When movable control rods are used, this means a large number of rods, which adds to cost; in some reactors the bumup obtainable is limited by the amount of room available for control rod insertion.

A fourth drawback of this simple batch irradiation is the waste of neutrons through absorption by boron at the beginning of the cycle. To give a rough example, to obtain an average bumup of 20,000 MWd/MT in a PWR with simple batch irradiation, it is necessary to absorb around 16 percent as many neutrons in boron at the beginning of life as are absorbed by 235 U at that time. In some of the more sophisticated methods of fuel management, these neutrons would be absorbed in 233 U to make plutonium. As the heat of fission is around 1 MWd/g and as about 0.8 g 23SU is fissioned per gram of 23SU consumed, (0.16X1/0.8) = 0.2 g plutonium/MWd of heat could have been made with 238 U that are not made with boron. As plutonium has a value of around $20/g, production of plutonium with these excess neutrons would be worth $4/MWd of heat, or 0.5 mills/kWh of electricity in a nuclear power plant that is 30 percent efficient. At the end of fuel life this loss drops to zero, so that over fuel life the average loss due to absorbing neutrons in boron is about 0.25 mills/kWh. In a 1000-MW plant operating 7000 h/year, this is a loss of almost $2 million/year, enough to make more sophisticated methods of fuel management well worth using.